EarthquakeProtectionofExistingStructureswithLimited …downloads.hindawi.com/journals/ace/2018/6019495.pdf · 2019-07-30 · control strategy combining the conventional base isolation

Research ArticleEarthquake Protection of Existing Structures with LimitedSeismic Joint Base Isolation with SupplementalDamping versus Rotational Inertia

Dario De Domenico and Giuseppe Ricciardi

Department of Engineering University of Messina 98166 SantrsquoAgata Messina Italy

Correspondence should be addressed to Dario De Domenico dariodedomenicounimeit

Received 28 August 2017 Revised 11 December 2017 Accepted 12 December 2017 Published 19 March 2018

Academic Editor John Mander

Copyright copy 2018 Dario De Domenico and Giuseppe Ricciardi ampis is an open access article distributed under the CreativeCommons Attribution License which permits unrestricted use distribution and reproduction in any medium provided theoriginal work is properly cited

Existing civil engineering structures having strategic importance such as hospitals fire stations and power plants often do notcomply with seismic standards in force today as they were designed and built based on past structural guidelines On the otherhand due to their special importance structural integrity of such buildings is of vital importance during and after earthquakeswhich puts demands on strategies for their seismic protection In this regard seismic base isolation has been widely employedhowever the existing limited seismic joint between adjacent buildings may hamper this application because of the large dis-placements concentrated at the isolation floor In this paper we compare two possible remedies the former is to providesupplemental damping in conventional base isolation systems and the latter consists in a combination of base isolation withsupplemental rotational inertia For the second strategy a mechanical device called inerter is arranged in series with spring anddashpot elements to form the so-called tuned-mass-damper-inerter (TMDI) directly connected to an isolation floor Severaladvantages of this second system as compared to the first one are outlined especially with regard to the limitation of flooraccelerations and interstory drifts which may be an issue for nonstructural elements and equipment in addition to disturbingoccupants Once the optimal design of the TMDI is established possible implementation of this system into existing structuresis discussed

1 Introduction

Passive vibration control systems of civil engineeringstructures and infrastructures are of utmost importance inearthquake-prone regions to mitigate or reduce damagepotential due to the shaking ground Evenmore importantlyseismic protection is imperative for those structures whoseintegrity during and after earthquakes is of vital importancefor civil and social purposes including hospitals fire sta-tions schools barracks power plants and so forth Nev-ertheless in many cases such structures present structuraldeficiency and do not comply with the requirements ofseismic standards in force today as they were designed andbuilt according to the past structural guidelines that were notas severe as the current regulations Consequently seismicprotection and retrofitting strategies of these structures are

highly desirable which should do not interfere with theoperational and functionality aspects of the building

In this regard seismic base isolation [1 2] has beenwidely employed along with energy dissipation systems[3 4] ampe lengthening of the first-mode period combinedwith the damping features provided by the base isolationsystem (BIS) significantly reduces the earthquake-inducedforces in the superstructure which can be designed to re-main in the elastic regime As a counter effect most of theearthquake-induced displacement demand is concentratedat the isolation floor which undergoes large displacements(whose magnitude depends on the design value of the BISeffective period) ampis has important implications in theretrofitting costs as large-size isolators should be adoptedthat can accommodate the required displacements in ad-dition to considering costly flexible connections for utilities

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 6019495 24 pageshttpsdoiorg10115520186019495

(eg waterworks gas fittings and electrical conduits) Inmost cases this implies a complete refurbishment of theexisting more rigid pipelines which significantly increasesthe overall retrofitting costs In addition an adequate sep-aration distance between adjacent buildings also calledseismic joint must be present in order to prevent mutualcollisions or structural pounding [5] ampe latter aspect maylimit the base isolation applications in those cases involvinga limited space between adjacent buildings as the actualseismic joint may easily be exceeded by the design dis-placement of the BIS amperefore the goal is to find a seismicprotection strategy such that the superstructure will expe-rience little damage but at the same time the overall dis-placement of the structure remains limited to withina reasonably acceptable threshold thus not exceeding theseismic joint Another problem that is often encountered inseismic base isolation is the vulnerability to long-periodground motions that might severely increase the lateraldisplacements of the isolators and cause long-lasting vi-brations due to the resonance effects [6] in a similar fashionto high-rise flexible-frame buildings [7 8]

ampese shortcomings have motivated the developmentof improved versions of the conventional base isolationscheme ampe most straightforward remedy for reducing theBIS displacement is to increase the isolation damping or toprovide supplemental damping Although this strategy doesreduce the excessively large displacements in the BIS it mayincrease the interstory drifts and floor accelerations in thesuperstructure [9] In addition to disturbing occupants thismay be an issue for nonstructural elements and equipmentthat could be of valuable importance in the above mentionedstrategic buildings (eg control centers real-time acquisi-tion data centers and so on) As an alternative a hybridcontrol strategy combining the conventional base isolationsystem with supplemental rotational inertia is proposed inthis paper In particular the BIS is coupled with the so-calledtuned-mass-damper-inerter (TMDI) ampe latter system byanalogy with the tuned mass damper (TMD) [10] consists ofmass spring and damper elements that are installed in serieswith a novel type of device the inerter [11] Details of thissystem will be discussed below

ampis paper compares the above two alternative strategiesfor the seismic retrofitting of existing buildings namelyseismic base isolation with supplemental damping versusseismic base isolation with supplemental rotational inertiaOptimal tuning parameters of the TMDI are detected withina probabilistic framework by considering the stochasticnature of earthquake ground motions and solving a non-linear optimization problem ampe earthquake ground mo-tion is modelled as a Gaussian process in the frequencydomain through the use of the power spectral density (PSD)function ampe influence of soil characteristics is investigatedby introducing three PSD functions representatives of firmmedium and soft soil conditions Based on the optimalparameters found a possible implementation scheme withregard to existing structures is proposed Some numericalapplications demonstrate advantages and disadvantages ofthe two vibration control strategies with regard to thestructural control of existing structures not only in terms of

displacement but also in terms of transmitted forces andother response indicators such as the base shear theinterstory drifts and the floor accelerations in order toevaluate the overall performance of these seismic protectionsystems

2 Inerter and Tuned-Mass-Damper-Inerter(TMDI)

ampe inerter element was introduced by Smith [11] in 2002 tocomplete the force-current analogy between mechanical andelectrical networks In particular the inerter has beenproposed as the mechanical counterpart of the capacitorconcept in electrical systems If u1 and u2 are the dis-placement coordinates of the two terminals connected by theinerter the following relationship holds for the ideal linearinerter

F b eurou1 minus eurou2( 1113857 (1)

where the constant of proportionality b is called inertanceand has dimensions of mass thereby it has been sometimestermed ldquoapparent massrdquo From (1) it is shown that theinternal force of the inerter is proportional to the relativeacceleration of its two terminals similarly to the damper andspring elements whose internal force is proportional to therelative velocity and displacement respectively

As schematically shown in Figure 1 the inerter can berealized through a two-terminal device that consists ofa combined arrangement of a rack pinions gears anda flywheel In this figure mf is the mass of the flywheel ri

and rpi denote the radius of gears and pinions respectivelyrf is the radius of the flywheel and rpf indicates the radius ofthe flywheel pinion Linear movement of the rack generatesrotational movement in gears and flywheel and the iner-tance of this system can be expressed as

b mf

r2f

r2pf1113945

n

i1

r2ir2pi

⎛⎝ ⎞⎠ (2)

where n is the number of gears amperefore this system isbased on the concept of rotational inertia Alternative re-alizations involve a rotary ball screw and a flywheel toconvert axial movement into rotary displacements ampeinerter has also been employed in the automotive sectorunder the name of J-damper for Formula 1 racing carsuspensions [12] By adjusting the gearing ratios or simplyintroducing additional gears it is possible to attain very highvalues of the inertance b without implying a large amount ofphysical mass mf In principle any desired value of b can beobtained with a device of reasonably compact form Suchmass amplification effect is the key feature of this system andmakes it appealing for vibration control purposes it has beendemonstrated that the apparent mass can be designed to beorders of magnitude (up to 200 times) higher than thephysical mass of the device ampis peculiarity has beenexploited in the context of enhancing the performance oftuned mass dampers (TMDs) In particular as sketched inFigure 2 the TMDI consists of an enhanced version of TMD(of mass mt spring stiffness kt and viscous damping ct)

2 Advances in Civil Engineering

in which an inerter device schematically represented by itsinertance is placed in between the TMD mass and theground (points 1 and 2) For the above mentioned char-acteristics the TMDI can be viewed as a lower mass andmore eective alternative to the traditional TMD wherethe device inertance plays the role of the TMD mass[13ndash16] While very large mass amounts are required for theTMD to achieve an acceptable vibration reduction eectivevibration control can be attained by the TMDI with rea-sonably limited physical mass Moreover while the TMDstroke is usually quite large the vibration reduction isattained by the TMDI without implying excessive stroke ofthe additional mass

Besides the optimal design of the TMDI which is de-scribed below in terms of its dynamic characteristics(stiness damping etc) there are a few practical consid-erations related to the functionality of the inerter that de-serve commentary Unlike mechanical networks involvingfrequent activity of the rack and pinion mechanism inearthquake engineering it is expected that the inerter ac-tually works just for few seconds that is during the seismicevent e horizontal accelerations transmitted by theshaking ground during this short time generate resistiveforces in the inerter by accelerating the internal wheelsHowever there may be an issue of backfeeding energy intothe structure when the building begins to slow down unlessan internal mechanism decouples the rotational mass to

prevent this phenomenon is energy is certainly trans-ferred from the inerter to the TMD therefore an adequatespace in the building is necessary to allow this strokeHowever this energy is not returned to the superstruc-ture since the inerter is not directly connected to it butjust to the TMD mass ere is an additional lterconsisting of the TMD spring and damper elementswhich signicantly reduce this backfeeding energy to thesuperstructure at the end of the earthquake is re-duction can be seen by the observation of the time historyof the response at the end of the seismic event (see below)Further investigation is certainly needed to carefullyanalyze these phenomena in more detail which is beyondthe main scope of this paper

3 Base Isolation with Supplemental RotationalInertia via TMDI

In the context of hybrid control strategies applications ofBIS in conjunction with a TMD attached immediately aboveor below the isolation oor of the building have been ex-tensively discussed in the literature [17ndash20] It has beenfound that by attaching a TMD to the BIS a certain re-duction of the displacement demand of a base-isolatedstructure is achieved depending on the TMD mass Con-versely applications of inerter-based devices in the contextof base-isolated structures are really few [21ndash25] To theauthorsrsquo best knowledge the dynamic layout of the BIScoupled with the TMDI has never been studied in the lit-erature as a seismic retrotting strategy of existing struc-tures which constitutes the main novelty of the presentresearch work In particular a practical implementation ofthis strategy is here proposed via the use of two sets ofisolators Besides the conventional isolators an auxiliary setof medium-to-high damping isolators are located un-derneath the structure the latter playing the role of damperand spring elements of the TMD Another important aspectthat has never been presented in previous studies is theoptimal design of this combined BIS +TMDI system andabove all the inuence of the soil conditions on the tuningparameters which is here dealt with within a wide para-metric study Due to the stochastic nature of earthquakeground motions such optimal parameters of the TMDI aresought within a probabilistic framework by minimization of

Terminal 1

u1 u2

Rotarymovement

Gear

r1

r2

rfrn

rpn mfrpf

rp2

rp1

Flywheel

Pinion

Terminal 2RackLinear movement

Figure 1 Schematic model of the inerter with rack and pinion mechanism

Inerter1

1 2

2

bt

ct

kt

mt

m1u1

ut

kt

ct

F = btuumlg

uumlg

Figure 2 Sketch of the tuned-mass-damper-inerter (TMDI)

Advances in Civil Engineering 3

the displacement variance Furthermore the performance ofthis system is assessed in terms of a variety of responseindicators that are useful and of practical importance fordesign engineers such as the base shear interstory driftsand oor accelerations

Due to the proportionality of the generated force of theinerter to the relative acceleration of its two terminals as per(1) this element can easily be incorporated into the equa-tions of motion as the inertance will only appear in the massmatrix In particular reference is made to the simple sketchshown in Figure 3 wherein a single degree of freedom(SDOF) structural system is base isolated and equipped witha TMDI attached to the isolation level e three degrees offreedom (DOFs) are the BIS displacement ub relative to theground the superstructure displacement usr relative to theBIS and the TMDI displacement ut relative to the groundLinear dynamical systems are considered with an equivalentlinear viscous damping idealization for BIS TMDI andsuperstructure e equations of motion of this simplied3-DOF system subject to a ground motion base accelerationeuroug(t) read

Meurou(t) + C _u(t) +Ku(t) minusτ euroug(t) (3)

with

M 1 1 0

1 1 + μb 0

0 0 μt + βt

C 2ζsωs 0 0

0 2ζbωbμb + 2ζtωtμet minus2ζtωtμet0 minus2ζtωtμet 2ζtωtμet

K ω2s 0 0

0 ω2bμb + ω2

tμet minusω2tμet

0 minusω2tμet ω2

tμet

τ 1

1 + μbμt

u usr(t)ub(t)ut(t)

(4)

and where the following positions in terms of frequencydamping and mass ratios of the three subsystems areintroduced

mtmb

cs

ms

ct

kt

ks

kb cb ug

ut

ub

us

usr

uumlg

large mass

base isolation system

structural SDOF

TMD

(a)

mt

mbbt

ms

kt

ks

ug

ub

us

ut

usr

uumlg

cs

kb cb

ct

F = btuumlg

Base isolation systemLimited flywheel mass

Structural SDOF

TMDI1

1

2

2

Inerter

(b)

Figure 3 Sketch of base-isolated structural SDOF with attached TMD (a) and with attached TMDI (b)


ωs

ks

ms

1113971

ζs cs

2msωs

ωb

kb

mb

1113971

ζb cb

2mbωb

ωt

kt

mt + bt

1113971

ζt ct

2 mt + bt( 1113857ωt

μb mb

ms

μt mt

ms

βt bt

ms

μet mt + bt

ms

met

ms

(5)

wherein bt and βt represent the TMDI inertance and theinertance ratio respectively while met is the effective mass ofthe TMDI that incorporates both the physical mass mt and theapparent mass bt (ie related to the rotary inertia as explainedabove)ampe limit case of a base-isolated structure with attachedTMD (Figure 3(a)) may be retrieved by assuming bt 0 ampeinertance ratio βt multiplies the relative acceleration betweenpoints 1 and 2 which coincides with eurout We point out thatwhile the inertial forces in the TMDI are associated with theeffective mass ratio μet the earthquake-induced accelerationson the right-hand side of (3) multiply the physical mass ratio μtonly (see the τ vector in (4)) amperefore due to the peculiarformat of (4) increasing the inertance βt ismore beneficial thanincreasing the TMD mass μt because it selectively raises theTMDI inertia properties without increasing the correspondingseismic force to which the device is subjectampis is an extremelyimportant consideration for limiting the TMDI stroke asdemonstrated and quantified below

4 Displacement Demand in Base-IsolatedStructures

In many existing structures the actual seismic joint is in-sufficient or nonexisting Indeed although modern codes

such as Eurocode 8 [26] prescribe a minimum seismic sep-aration distance between adjacent buildings large sections ofcities in seismically active regions were constructed beforesuch requirements were introduced [5]ampis problem is reallyimportant for strategic buildings in which during strongearthquake pounding damage caused to both structural andnonstructural components may have dramatic social and civilconsequences Moreover in big and highly populated citiesand metropolitan areas in which the cost of land is very highbuildings that are nearly in contact with each other thereforeprone to pounding damage are frequent

In order to mitigate the earthquake-induced damageto such buildings the strategy of seismic base isolationhas been widely adopted Nevertheless while reducing theforces in the superstructure there is an issue when theseismic joint is quite limited as in the cases mentionedabove Indeed the vibration control is achieved by pro-viding flexibility at the base of the structure such that theoverall displacement of the base-isolated structure mayalso exceed the maximum admissible displacement resultingfrom the actual seismic joint Just to fix the concepts wesuppose that the actual seismic joint is a fraction of thetotal height of the building H for example H100 InFigure 4 we extremely simplify the concept of displace-ment demand of a base-isolated structure and we presentthree different situations ampe first one (Figure 4(a))concerns a typical BIS having conventional parameters ofnatural period and damping ratio in this case the BISdisplacement ub may be higher than the admissible seismicjoint which may lead to pounding damage under a strongearthquake In the second situation (Figure 4(b)) the BISperiod is not so high which means that the flexibility of theisolators is reduced Although this may in turn reduce theBIS displacement ub so as to be lower than the seismicjoint the effectiveness of the vibration control achieved bythe BIS decreases because of the reduced period whichimplies higher forces and displacements transmitted to thesuperstructure As a matter of fact this seismic protectionsystem is not convenient and the displacements of thesuperstructure (eg the last floor displacement uslf ) mayalso exceed the seismic joint ampe third and final casedepicted in Figure 4(c) is related to a BIS endowed withhigh damping features (eg high-damping rubber-bearingisolators or high-performance lead rubber bearings) Inthis situation the displacements of both the BIS and thesuperstructure are quite limited and may be lower than theseismic joint Nevertheless increasing the BIS dampingmay be detrimental for the superstructure response interms of interstory drifts and floor accelerations which areof great importance for nonstructural components andequipment present in the building in addition to dis-turbing occupants [9] amperefore it seems that the con-ventional BIS alone is not capable of achieving an effectiveseismic protection and structural control of the buildingalong with guaranteeing quite limited displacements forexisting structures having limited seismic joint As clari-fied below enhancing the BIS with the supplemental ro-tational inertia via the concept of the TMDI could bea viable solution to this problem


5 Optimal Design of the TMDI and TuningProcedure

e selection of the BIS parameters follows the conventionalrules for seismic base isolation [1] for instance the naturalperiod of the BIS is assumed to be 5minus 10 times higher thanthat of the xed-base structure in order to achieve an ef-fective vibration isolation Conversely the design of theTMDI is not straightforward as the dynamic parameters ofthe TMDI should be tuned such that the best vibrationcontrol is attained An optimization problem is set up forthis purpose e optimization procedure here proposedresembles tuning procedures for TMD-based controlstrategies [10 20 27 44] wherein some parameters are thefree design variables sought in the optimization problemwhile other parameters are supposed known

e TMDI is characterized by four parameters in themost general case namely μt βtωt and ζ t Among these

four parameters the approach pursued in this paper is tond the best frequency ratio ]t ωtωb and the best TMDIdamping ratio ζt for xed eective mass ratio μet μt + βtwhich is similar to other research contributions dealing withinerter-based devices in broad terms [14 15] Indeed theeective mass ratio μet can be designed according to me-chanical considerations that is via the selection of a ywheelmass μt and an inertance ratio βt arising from (2) and Figure 1For a given μet the optimal couple (]t ζt) is sought thatminimizes an objective function or performance index Sucha performance index being a representative measure of thesystem response is chosen via a stochastic dynamic analysisof the system thus accounting for the stochastic nature ofthe earthquake ground motion as described below

51 Earthquake Input Representation Owing to the sto-chastic nature of earthquake ground motion [28] the base

H

Displacement profile ofbase-isolated structure

Seismic jointof existing structure(eg H100)

uslf

ub

(a)



uslf

ub

H

(b)



Nonstructual component

Sensitive equipment

High-flooraccelerations

uslf

ub

H

(c)

Figure 4 Schematic representation of the displacement demand in base-isolated structures (a) conventional BIS with medium damping(b) low-period BIS with medium damping (c) high-damping BIS


acceleration euroug(t) entering (3) is assumed as a randomprocess more specically a quasi-stationary (uniformlymodulated) Gaussian zero-mean stochastic process de-scribed by the two-sided evolutionary PSD function [29 30]

S euroug(ω t) |φ(t)|2S(ω) (6)

e time-modulating function by Hsu and Bernard[31] is adopted

φ(t) a1t exp minusa2t( ) (7)

in which the two constants have been set as a1 045 sminus1 anda2 16 sminus1 in accordance with statistical studies regardingthe general class of accelerograms recorded during the SanFernando California earthquake [32]

In order to investigate the inuence of soil characteristics interms of frequency content a ltered Gaussian white-noiseprocess is considered for the stationary PSD function S(ω)entering (6) [33] e widely used Kanai-Tajimi lter model[34 35] is employedwith a second lter in series as proposed byClough and Penzien [32] in order to overcome the unreal-istically high values of the PSD in the low-frequency regime

S(ω) ω4g + 4ζ2gω

2gω

2

ω2g minusω2( )

2 + 4ζ2gω2gω2

ω4

ω2f minusω2( )

2+ 4ζ2fω2

fω2Sw

(8)

where ωg and ζg are the fundamental circular frequency anddamping ratio of the surface soil deposits respectively andωf and ζf represent the additional CloughndashPenzien lterparameters that control suppression of the low frequenciesallowed by the KanaindashTajimi spectrum e Sw parameter in(8) describing the amplitude of the bedrock excitationspectrum modelled as a white-noise process can be relatedto the peak ground acceleration (PGA) euroug0 according to theformula [36]

Sw 0141ζg eurou

2g0

ωg1 + 4ζ2gradic (9)

Filter parameters ωg ζgωf and ζf should be appro-priately selected depending on the soil condition beingconsidered Herein we assume deterministic values of thelter parameters that are related to the soil stiness accordingto the study by Der Kiureghian and Neuenhofer [37] erelevant values for rm medium and soft soil conditions arereported in Table 1 In Figure 5 the corresponding evolu-tionary PSD function is plotted for the three analyzed soilconditions by assuming a PGA equal to euroug0 03g Rea-sonable PSD shapes result from the assumed lter parametersfor instance the PSD for the soft soil produces a relativelynarrow-band process with a predominant period of ap-proximately 125 s which might be representative of deepalluvium sites such as parts of Mexico City whereas thespectral shape for the rm ground is broadband and containssignicant contributions from higher frequencies

52 Objective Function and Numerical Algorithm Optimumdesign of the novel vibration control system is based on thestochastic response of the 3-DOF system due to the PSDfunction (8) thus relying on a probabilistic frameworkWithreference to the simplied 3-DOF system sketched in Figure3 a representative measure of the system response is thevariance of the displacement of the structural SDOF relativeto the ground that is of the variable us usr + ubereforethe objective function (OF) to minimize is

OF σ2us E u2s[ ] σ2usr + σ2ub + 2σusrub (10)It will be demonstrated that minimizing σ2us has a twofold

eect namely reducing the displacement in the BIS ub andlowering the relative displacement between the super-structure and the BIS usr

Table 1 Filter parameters depending on soil conditions (Der Kiureghian and Neuenhofer [37])

Soil type ωg (rads) ζg ωf (rads) ζfFirm 150 06 15 06Medium 100 04 10 06Soft 50 02 05 06

030

002

520

004

43

006

10 210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(a)

030

004

20

008

54

012

10 3210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(b)

030

012

20

024

54

036

10 3210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(c)

Figure 5 Evolutionary PSD function as per (6) for three soil conditions (a) rm (b) medium (c) soft


e optimization problem dealt with in this paper ishandled via a numerical search algorithm through the built-in MATLAB fmincon function which is a nonlinearprogram solver (adopting the interior-point algorithm) withembedded constraint functions for the sought TMDI tuningvariables x []t ζt] e lower bound and upper boundvectors are assumed as (in MATLAB vector notation) xlb [010 001] and xub [200 100] e tuning variables ]tand ζt span their allowed ranges with an increment of 10minus7and the tolerance on the achieved minimum OF is 10minus7 Inmathematical terms the following nonlinear constrainedsingle-objective multivariable optimization problem is to besolved

minx

σ2us(x) such that xlb lexle xub (11)

53 Parametric Study e optimal design of the TMDI toachieve a reduction of the displacement demand in a base-isolated structure is discussed here A wide parametric studyis carried out wherein the main investigated parameters are(1) the soil condition (rm medium soft type and the

white-noise process as an extremely broadband frequencycontent) (2) the physical mass ratio μt (3) the inertance(or apparent mass) ratio βt and (4) the BIS damping ratio ζbe damping ratio of the structural SDOF is assumed asζs 002 which is a rather typical value if limited damage isexpected in the superstructure Moreover an isolation ratioin terms of frequency ratio ]b ωbωs 02 and a mass ratioμb 02 have been assumed throughout

In Figures 6ndash9 the optimal TMDI parameters are shownfor rm medium soft soil conditions and for a white-noise(broadband) earthquake input A value of ζb 02 is hereassumed as the inuence of ζb is analyzed later For practicalpurposes the minimum achieved σ2us value is shown nor-malized with respect to the case without TMDI that is thedisplacement variance of the structural SDOF in a conven-tional base isolation scheme σ2us0 As a result values of theσ2us σ

2us0

ratio lower than the unity means that the proposedcontrol strategy is eective in the displacement reductionwith (1minus σ2us σ

2us0) times 100 being a percentage measure of such

reduction e design graphs also include the limit case ofthe TMD in place of the TMDI for a zero value of theinertance ratio that is βt 0ree dierent values of the μt

0 01 02 03 04 05 060

02040608

1

βt

μt = 001μt = 01μt = 04

Firm soil conditions

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

βt

μt = 001μt = 01μt = 04


ν t op

t=ϖ t

opt

ϖb

(b)

0 01 02 03 04 05 060

01

02

03

04

βt

μt = 001μt = 01μt = 04


ζ t op

t

(c)

Figure 6 Optimal TMDI tuning for rm soil conditions (a) minimum OF achieved normalized with respect to the case without TMDI(b) optimal frequency ratio (c) optimal damping ratio

0 01 02 03 04 05 060

02040608

1

βt

μt = 001μt = 01μt = 04

Medium soil conditions

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

βt

μt = 001μt = 01μt = 04


ν t op

t=ϖ t

opt

ϖb

(b)

0 01 02 03 04 05 060

01

02

03

04

βt

μt = 001μt = 01μt = 04

Medium soil conditionsζ t

opt

(c)

Figure 7 Optimal TMDI tuning formedium soil conditions (a) minimumOF achieved normalized with respect to the case without TMDI(b) optimal frequency ratio (c) optimal damping ratio


ratio are shown namely μt 001 that is representative ofa small-mass ywheel device as shown in Figure 2 μt 01that is relevant to a conventional TMD system and μt 04representing a nonconventional TMD that exploits massesalready present in the system [15 38]

By inspection of the OF achieved the TMDI appears tobe very eective in the displacement reduction of the base-isolated structure In particular depending on the soilconditions a 60ndash70 reduction of the displacement varianceis achieved with an inertance ratio βt 04 whereas thedisplacement reduction attained by a nonconventional TMDhaving μt 04 is slightly lower (cf the values at the in-tersection with the vertical axis limit case βt 0) Howeverwe stress that high values of the inertance ratio βt can beaccomplished without increasing the inerterrsquos physical massbut rather via the adjustment of the gearing ratios (or simplyby setting two or more ywheels in series [16]) is meansthat high vibration control performance can be achieved bythe TMDI without resorting to excessively large secondarymass as implied in the nonconventional TMD In otherwords the TMDI outperforms the classical TMD as it

exploits the light-weight features of the conventional TMDwith the eectiveness of the nonconventional TMD [15]

e optimal TMDI parameters ]topt and ζtopt are sig-nicantly aected by the physical mass μt and by theinertance ratio βt Generally speaking for all the soil con-ditions ]topt decreases with increasing μt and with in-creasing βt Conversely the optimal damping ratio ζtoptfollows an opposite dierent trend that is it increases withboth increasing physical mass andor apparent mass einuence of the soil condition is considerable the soilstiness leads to higher frequency ratios ]topt and lowerdamping ratios ζtopt and this variability turns out to bemoreimportant when high values of μt or βt are consideredInterestingly the optimal parameters found under thewhite-noise assumption are nearly similar to those obtainedfor soft soil conditions Finally the vibration control per-formance of the system reduces when passing from rm tosoft soil conditions this is consistent with the expectationsas the soft soil condition leads to a predominance of long-period components (such as that obtained in Mexico City)e assembled base-isolated system is rather vulnerable to

0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04

So soil conditions

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04

So soil conditions

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04

So soil conditions

βt

(c)

Figure 8 Optimal TMDI tuning for soft soil conditions (a) minimum OF achieved normalized with respect to the case without TMDI(b) optimal frequency ratio (c) optimal damping ratio

0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04

White-noise assumption (extremelybroadband frequency content)

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04


βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04


βt

(c)

Figure 9 Optimal TMDI tuning for white-noise assumption for the earthquake (a) minimum OF achieved normalized with respect to thecase without TMDI (b) optimal frequency ratio (c) optimal damping ratio


earthquake excitations whose frequency content is con-centrated in the long-period range [6]

e inuence of the BIS damping ratio ζb is investigatedin Figures 10 and 11 Two ζb values are analyzed namelyζb 01 representative of low-damping rubber bearings(LDRBs) and ζb 03 typical of high-damping rubberbearing (HDRB) as well as of lead rubber bearings (LRBs) Inaccordance with other literature ndings related to TMD-based systems [18] it is found that the eectiveness of theTMDI increases when low-damping isolation bearings areaddressed (cf Figure 10(a)) For instance adopting βt 02the reduction of the displacement variance is more thandoubled in passing from ζb 03 to ζb 01 regardless ofthe soil condition (cf Figure 10(a))

Furthermore this reduction is not conned to thedisplacement variance In Figure 11 we also report thesuperstructure total acceleration variance computed asσ2eurous tot E[eurou

2s tot] 4ζ2sω

2sσ

2_usr+ ω4

sσ2usr and the variance of the

TMDI displacement σ2ut characterizing the so-called TMDIstroke Normalization of these quantities is again performed

e TMDI displacement variance shown in a semilog plotfor improved readability is divided by the BIS displacementvariance in the uncontrolled case σ2ub0 To make the resultsmore evident a thicker solid horizontal line is drawn ata unitary value of the normalized TMDI stroke to distinguishbetween amplication and reduction as compared to theconventional base isolation scheme

It can be noted that the reduction of the superstructureacceleration is improved when low-damping isolators areemployed (Figure 11(a)) Similar eects are observed withregard to the TMDI stroke the displacement of the sec-ondary mass is more eectively controlled for low-dampingBIS because the range of displacement reduction widenswhen lowering the ζb value and the attained σ2ut valuedecreases accordingly (Figure 11(b)) It seems that theinertance ratio should be set such that βt gt 03 in order toachieve an eective vibration control of the base-isolatedstructure (in terms of displacements and accelerations)without implying a large TMDI stroke Looking at theobtained graphs βt 04 seems to be a reasonable inertance

0 01 02 03 04 05 060

02040608

1

FirmMediumSoWhite-noise

ζb = 01 (LDRB)FirmMediumSoWhite-noise

ζb = 03 (LDRB)

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06025

03

035

04

ν t op

t=ϖ t

opt

ϖb



ζb = 03 (LDRB)

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t



ζb = 03 (LDRB)

βt

(c)

Figure 10 Optimal TMDI design for dierent BIS damping ratios and soil conditions (a) minimum OF achieved normalized with respectto the case without TMDI (b) optimal frequency ratio (c) damping ratio

0 01 02 03 04 05 060

02

04

06

081

σ2uuml s t

otσ

2 uuml s0 to

t

βt

ζb = 01FirmMediumSoWhite-Noise

ζb = 03FirmMediumSoWhite-noise

(a)

001

01

10

1

50

0 01 02 03 04 05 06βt

Stro

ke =

σ2 u tσ

2 u b0

Displacement reduction

Displacement amplification


ζb = 03

MediumSoWhite-noise

Firm

(b)

Figure 11 Optimal TMDI design for dierent BIS damping ratios and soil conditions (a) normalized total acceleration variance and(b) normalized TMDI displacement variance representative of the TMDI stroke


ratio for design purposes All the aspects discussed in thisparametric study are of extreme importance for a practicalimplementation of this system into existing structures aswill be clarified in the following sections

6 Implementation of the Proposed System intoExisting Structures

ampeoptimal tuning of the system discussed in Section 5 is thestarting point for a practical implementation of the proposedsystem into existing structures which is the main goal of thisresearch work ampe analysis is here extended to multi-degree-of-freedom (MDOF) systems like multistory build-ings To this aim the superstructure DOF is meant as thefundamental mode of vibration of the superstructure Moreimportantly a possible strategy of implementation intoexisting structures comprising an additional set of isolatorsto attach the inerter to the structure is presented here ampeaspects discussed in Section 53 are briefly summarized hereIt has been found that the for firm soil conditions theoptimal TMDI frequency should be higher than that for thesoft soil conditions On the contrary it seems that theoptimal TMDI damping ratio is lower for the firm soilconditions than that for the soft soil conditions ampe in-fluence of the soil condition on the TMDI optimal design ismore pronounced for high values of μt or βt Moreover aninertance ratio at least βt 035minus 04 is essential for keepingthe TMDI stroke limited

For a possible implementation strategy of this systeminto existing structures we now approach the problem ofdesigning the base isolation system from a different per-spective ampe elastic and damping properties of the TMDIsystem kt and ct may be meant as the effective stiffness andequivalent viscous damping ratio of an auxiliary set ofisolators acting in parallel with the conventional isolatorsthe latter is featured by corresponding kb and cb assketched in Figure 12 ampe only difference between thesetwo groups of isolators is that the auxiliary isolators areequipped with an inerter device which connects them tothe ground amperefore this model idealization representsan enhanced base-isolation system with a particular ar-rangement of conventional isolators auxiliary isolatorsand inerter ampis schematic arrangement is a possibleimplementation strategy of the proposed system intoexisting structures In this way the inerter can easily beconnected to the structure via the auxiliary isolators anda sliding device ampe mass mt comprises the flywheel massand the mass of the rigid element that connects the aux-iliary isolators with each other for example a basementsubunit On the basis of the optimal TMDI parametersfound in Section 53 the auxiliary isolators should be moreflexible (ωtopt asymp 035ωb) and should have more inherentdamping (ζtopt asymp 02minus 03) than the conventional isolatorsin order for the proposed system to perform at its bestBased on these considerations a new strategy of seismicretrofitting of existing structures is proposed in this paperthat consists in a combination of low-damping conven-tional isolators for example ζb asymp 01 in parallel withmedium-to-high damping flexible auxiliary isolators for

example ζt asymp 01 the latter installed in conjunction with aninerter device having inertance ratio around βt 04

To summarize the basic steps of a schematic seismicretrofitting procedure via the proposed system discussedabove in Figure 13 a conceptual flowchart is elaboratedObviously this flowchart is an extremely simplified ide-alization of the several complex design stages for a realseismic retrofitting procedure A series of bullet pointshighlight the main procedural steps in a schematic wayOnce a given existing structure is characterized in terms ofdynamic properties soil conditions and importance factorthe design of the retrofitting system is normally based onconstraints such as a limited seismic joint or the presence ofadjacent buildings First the set of conventional isolators isdesigned As a second step the properties of the inerterdevice are chosen on the basis of an expected value of theperformance index which is in turn related to the desiredlevel of vibration reduction to achieve For given propertiesof the inerter device in terms of mass and rotational inertia(inertance) the set of auxiliary isolators are designed on thebasis of the design graphs discussed in Section 53 Anoverall check of the entire system should be made via time-history linear or nonlinear analyses employing designearthquakes that are relevant to the installation site soilconditions and importance factor of the building ampeverification is made with respect to both displacements andstress in the superstructure Unsatisfactory displacementreduction (eg it is found that the displacements stillexceed the seismic joint) may be faced via increasing theinertance properties (mass and rotational inertia) whereasthe presence of high stresses in the superstructure(eg bending moments tensile forces floor accelerationsfor sensitive equipment and so forth) can be avoidedthrough a global amendment of the base isolation system asa whole including the dynamic characteristics of con-ventional isolators and the resulting properties of auxiliaryisolators and the inerter

7 Base Isolation with Supplemental Dampingversus Supplemental Rotational Inertia

In line with the conceptual flowchart introduced in Figure13 in this section we check the effectiveness of the proposedseismic retrofitting procedure via time-history analyses Two

Structural SDOF(1st vibration modeof MDOF systems)

Enhanced baseisolation system

Conventionalisolators (low damping)

Auxiliaryisolators(flexibility high damping)

ms

csks

kt ctkb cb

mb

mt

bt

uumlg t

Figure 12 Schematic arrangement of the proposed base isolationsystem comprising two sets of isolators to attach the inerter to thestructure


different strategies are analyzed and compared namely theseismic base isolation with supplemental damping and theseismic base isolation with supplemental rotational inertiaby means of the TMDI A third vibration control systemcombining the seismic base isolation with an attached TMDis also discussed as the limit case of the TMDI for a zerovalue of inertance that is by setting bt 0

71 Numerical Application ampe existing structure is a five-story reinforced concrete (RC) building For simplicity weassume that the building is symmetric in plan so that it canbe analyzed through the equivalent planar frame depicted

in Figure 14 Obviously un-symmetric plan buildings aremore realistically found as existing structures which re-quires a 3D model instead of a planar frame However theaim of this paper is just to present and compare differentseismic retrofitting strategies therefore a quite simplestructure and a planar model are not expected to majorlyprejudice the generality of the discussion

According to Eurocode 8 requirements [39] in-formation for structural assessment should be collectedfrom original outline construction drawings survey in situinspection in situ testing via destructive- andor non-destructive tests and so forth Geometric data regardingcross-sectional properties of beam and column elements

Input data of the existing structure

bull Dynamic properties mass damping and stiffness matrices Ms Cs Ks bull Soil conditions (firm soil so deposits etc)bull Seismic joint or maximum admissible displacement s (eg s =H100)bull Constraints (eg adjacent buildings and presence of sensitive equipment)bull Importance factor of the building rarr desired level of seismic protection

Design Of Conventional Set Of Isolators

bull Modal analysis of the fixed-base structure rarr compute T1bull Select a TbT1 ratio (eg 5ndash10) depending on constraints and importance factorbull Select a ζb ratio (assume low damping eg ζb = 01 as a preliminary choice)

check for displacementsus max lt s

EXIT

Design of the inerter devicebull Based on the building importance factor (desired level of seismic protection) select the ideal values of mt and bt via the design graphs of the performance index

Design of auxiliary set of isolators

bull Select a ωtωb ratio based on the design graphs from the optimization problembull Select a ζt damping ratio based on the design graphs from the optimization problem

Time history analysis and verificationbull Check the level of vibration reduction via time-domain (linear andor nonlinear) analyses with design earthquake ground motionsbull Check the feasibility and cost-effectiveness of the system in terms of TMDI stroke

Yes

No

check for stressin the super structure

YesNoIncrease the isolation ratio of theconventional isolators TbT1 Increase the damping ratio ζb

Increase the inertance btandor the mass mt

Seismicretrofitting

Figure 13 Conceptual flowchart of a seismic retrofitting procedure based on the proposed system of Figure 12


are reported in Figure 14 We assume that bay width L andcolumn heightH are constant at every story with L 45mand H 32m e elastic modulus of the material is E 26000MNm2 [40] e second-moment of the cross-sectional area is computed according to the column andbeam sections reported in Figure 14 A static condensationmethod is applied in order to eliminate the (zero-mass) ro-tational DOFs [41] With axial deformations in beams andcolumns neglected the frame has 35 DOFs with 5 dynamicDOFs represented by the displacements of the 5 storiesrelative to the BIS e mass of the superstructure is thuslumped at the oor level with msj 60000kg denoting themass for the rst 4 oors (j 1 4) andms5 50000kgfor the fth oor Considering the importance factor of thebuilding the actual seismic joint and the presence of non-structural equipment the following constraints shouldbe met

maximum displacement(or drift index) usmax lt s

with s H

100 016 m

maximum interstory drift indexΔhH

030⟶Δhlt 00096 m

maximum floor acceleration eurousmax lt 02 g(12)

In a seismic retrotting procedure the description of theseismic motion may be made by using articial accelero-grams and recorded or simulated accelerograms [25] that are

consistent with the soil characteristics of the installation siteIn this paper articial samples are generated in accordancewith the evolutionary PSD function dened in (6) by meansof the superposition of N harmonic waves through thespectral representation method [42]

eurou(r)g (t) φ(t)2

radicsumNminus1

i0

2S(iΔω)Δωradic

cos iΔωt + ϕ(r)i( ) (13)

where ϕ(r)i are the independent random phases uniformlydistributed over the interval [0 2π] Δω ωcN with ωcbeing the upper cuto frequency beyond which S(ω) asymp 0

We assume that the building is installed in rm soilconditions According to the Monte Carlo method an en-semble of 100 articial uniformly modulated accelerogramsis generated from the rm-soil evolutionary PSD functionpresented in Section 51 (time duration of 30s and PGAequal to euroug0 02g are assumed) Time-history analyses arecarried out via direct integration of the equations of motionand the relevant statistics of the structural response areevaluated by averaging the results

Following the conceptual owchart of Figure 13 oncethe input data of the existing structure are established themodal analysis of the xed-base structure is carried outwhich leads to the determination of the natural periodsTsi[s ] [0501 0189 0112 0079 0056] and the partici-pating mass ratios ϵsi[ ] [8177 1067 396 255 104]From Figure 14 the base isolation system relevant to theplanar frame under study is composed of an ensemble of 6isolators two of which (the so-called auxiliary isolators) aresmaller in size (ie more exible) and equipped with ro-tational inertia via an inerter device e basement mass isset as mb 50000kg hence resulting in a mass ratioμb ≃ 017 As a preliminary choice we assume an eectiveperiod of the conventional isolators Teff 2s and an

H = 32 hc = 06

hc = 06

hc = 06

hc = 05

hc = 04

hb = 06

hb = 06

hb = 07

hb = 07

hb = 07

h b

h c

hc

H = 32

H = 32

H = 32

H = 32

Beamsection

03

0303

kb cbkt ct

bt

L = 45 L = 45 L = 45

Columnsection

L = 45 L = 45

Figure 14 Five-story RC building with the seismic protection system proposed in this paper (all dimensions in m)


equivalent viscous damping ratio ζb 01 which implies theuse of low-damping rubber bearings in line with the pre-vious remarks Note that Teff is related to ωb via the ex-pression Teff Tb

1 + μminus1b

1113969with Tb 2πωb which is due

to the definition of ωb made in (5) Based on the designgraphs developed in Section 53 the inerter is designedsuch that βt 04 and μt 001 Considering the total massof the superstructure this implies that mt 2900kg andbt 116 000kg ampe damping coefficients of the super-structure are assumed to be stiffness-proportional (ldquoclassi-cally damped systemrdquo) with ζsi 002 with i 1 5 Allthese data serve to detect the optimal frequency anddamping ratio of the TMDI via the design graphs developedin Section 53 ampe following optimal parameters are foundωtopt 2502 rads and ζtopt 0256 For comparison pur-poses the base isolation system with attached TMD is alsostudied by assuming βt 0 and μt 01 and the optimalparameters found are ωtopt 2713 rads and ζtopt 0135Alternative seismic retrofitting strategies investigated beloware the conventional base isolation system (without TMDIsystem) equipped with supplemental damping instead ofrotational inertia To this aim we have considered increasingvalues of the BIS damping ratio namely ζb 03 andζb 04 Overall five different seismic retrofitting strategiesare analyzed as summarized in Table 2

ampe results from 100 time-history analyses (each relevantto a given accelerograms) are averaged to obtain the meanroot-mean-square (RMS) values and the mean maximum(MAX) values of a few representative response indicatorsthat are reported in Tables 3 and 4 respectively A selectionof response indicators that are useful and of practical im-portance for design engineers is computed for the fiveretrofitting systems including the last-floor displacementus5 the second interstory drift Δus2 us2 minus us1 the fourthfloor acceleration eurous4 the base shear Vb sumiω2

sic2sidsi the

superstructure kinetic energy Ts 12 _uTs Ms _us the super-

structure elastic strain energy Es 12uTsrKsusr the BIS

displacement ub and the TMDITMD stroke ut In this wayan overall assessment of the performance of each seismicretrofitting strategy is made for a consistent comparisonPercentage of reductions achieved as compared to theconventional base isolation scheme (reference solution) isreported in brackets a negative value indicates reductionand a positive one means amplification By inspection of theTable 3 and Table 4 it is found that the best seismic ret-rofitting strategy is the BIS with supplemental rotationalinertia (TMDI) that achieves an excellent level of vibrationreduction not only in terms of displacement demand of thebase isolation system (with reductions of almost 55 for the

RMS values and of 43 for the MAX values) but also withregard to all the other response indicators of the super-structure For example the kinetic energy is brought downof about 75 and 60 when the RMS and MAX values areconsidered respectively Similar considerations may bedrawn for the base shear with reductions of 53 and 38

Such performance of the system 2 is achieved withoutrequiring large physical mass and without implying exces-sively large TMDI strokes indeed the displacements of theauxiliary isolators are reduced of around 26 and 15 (RMSand MAX values resp) as compared to the displacement ofthe conventional BIS in the uncontrolled case ub0 whichmakes the proposed system very convenient for practicalapplications Conversely if the BIS is combined with a TMD(system 3) the vibration reductions of all the response in-dicators are considerably lower than those of the previous casewith the TMDI Additionally the vibration control is ac-complished at the expense of very large TMD strokes withvalues of ut even higher (not lower) than 100 in comparisonwith the BIS displacement ub0 of the uncontrolled case(maximum displacement achieved is 48cm) ampis means thata large space in the building should be devoted to the TMD inorder to accommodate the displacement demand of thissecondary mass ampis makes the difference between a passivevibration control system equipped with large mass and a oneendowed with large rotational inertia (inertance) with thelatter selectively raising the inertia properties without am-plifying the corresponding seismic force to which the device issubject but rather suppressing the level of ground shakingAdditionally it is reasonably expected that using an inerterwith large inertance ratios is by far cheaper than employinga TMD with very large mass amounts ampis aspect may haveimportant implications in the potential construction costs ofthese two alternative systems Finally the analysis of theresults achieved by the systems 4 and 5 namely the BISwith supplemental damping reveals a poorer performancethan system 2 in terms of RMS and MAX values and withregard to all the analyzed response indicators despite the veryhigh values of damping ratios adopted For instance thesecond interstory drift is reduced to around 40 and 28(RMS and MAX values resp) as compared to the conven-tional BIS while system 2 with rotational inertia attainsa reduction of 52 and 37

In Figures 15(a) and 15(b) two arbitrary time histories ofthe last-floor displacement response (picked out from the100 time-history responses for the 50th and 100th groundmotion of the ensemble) are illustrated ampese plots revealthat in order for the TMDTMDI to be fully effective theseismic input energy should penetrate into the system

Table 2 Seismic retrofitting strategies analyzed and compared in this study and optimal parameters

Seismic retrofitting label Seismic protection strategy ζb Teff (s) ζt ωt (rads)1 Conventional BIS 01 20 mdash mdash2 BIS with rotational inertia (TMDI) 01 20 0256 25023 BIS with TMD 01 20 0135 27134 BIS with supplemental damping 03 20 mdash mdash5 BIS with supplemental damping 04 20 mdash mdash


gradually so that there is time for transfer of energy from thebase-isolated structure to the secondary system which wasalso observed in [18] is implies that the eectiveness ofthe TMDI can be jeopardized if the accelerogram has a highimpulsive content in the rst instants of motion [15] Alsoreported in Figures 15(c) and 15(d) are the displacements ofthe secondary mass (TMD TMDI) It is seen that the TMDdisplacements may be disproportionately large exceedingthe maximum displacement of the BIS in the uncontrolledcase On the contrary the displacements of the TMDI arereasonably limited

One possible drawback of the proposed system withrotational inertia could be the generated force which isproportional to the relative acceleration To assess the in-cidence of this force in Figure 16 for the same two accel-erograms discussed above we display the time histories ofthe reactive forces generated in the system In particular wecompare the damping force in the conventional isolatorscomputed as F cb _ub with the reactive force in the inerter-based device computed as F bt eurout It is found that the latterforce is higher than the damping force of a low-dampingsystem of isolators with ζb 01 but is roughly comparable

to the damping force exerted in the system 5 that is the BISwith supplemental damping which however yields a poorervibration reduction according to Tables 3 and 4 Consideringthis fact it is more convenient to adopt a seismic retrottingstrategy with BIS coupled with rotational inertia rather thansupplemental damping However it is important that all theelements that connect the inerter device to the structuremust resist the forces arising from the above calculation andtherefore the use of sti supports is highly recommended

e verication procedure of the constraints listed in(12) is carried out in a graphical way in Figure 17 In par-ticular the average maximum distribution proles of thehorizontal displacements the inerstory drift index and theoor accelerations are shown along the height of thebuilding and compared to the threshold values indicated in(12) which are reported as a thicker solid line As expectedwhile the displacement constraint is met by the xed-basebuilding the conditions on the interstory drift and ooracceleration are largely exceeded is means that anearthquake protection system should be adopted econventional BIS (with low-damping ζb 01) violatesthe conditions on displacements and oor accelerations

0acc 50

5 10 15 20 25 30ndash04

ndash02

0

02

04u s

5 (m

)

t (s)

Conventional BISBIS with TMDBIS with supplemental dampingBIS with rotational inertia (TMDI)

(a)

acc 1000 5 10 15 20 25 30

ndash025

ndash015

ndash005

005

015

025

u s5

(m)

t (s)


(b)

acc 500 5 10 15 20 25 30

ndash06

ndash03

0

03

06

u t (m

)

t (s)

ub conventional BISBIS with TMDBIS with TMDI

(c)

0 5 10 15 20 25 30ndash04

ndash02

0

02

04

u t (m

)

t (s)


acc 100

(d)

Figure 15 Time-history response of the RC building shown in Figure 14 subject to two arbitrary articial accelerograms (a b) last-oordisplacement (c d) secondary system (BIS TMDI TMD) displacement


Increasing the BIS damping up to ζb 04 thus consideringa BIS with supplemental damping reduces the displace-ments down to an acceptable level lower than the thresholdvalue but the floor accelerations are still larger than themaximum admissible ones On the contrary the BIS withrotational inertia satisfies all the three constraints

ampe analysis discussed above has been carried out bymeans of uniformly modulated accelerograms as anidealization of real accelerograms that are actually fullynonstationary in nature To corroborate the conclusionsof the present investigation we repeat the analysis withtwo natural earthquake ground motions to scrutinize theeffectiveness of the seismic retrofitting strategies whileaccounting for the fully nonstationary character ofthe seismic input Two recorded accelerograms are se-lected from the Center for Engineering Strong Motion Data

(httpstrongmotioncenterorg) namely El Centro (18 May1940 epicenter distance from recording station 17 km) andLoma Prieta (17 October 1989 epicenter distance from re-cording station 7 km) ground motions Relevant results arepresented in Figure 18 for the time histories of the last-floordisplacement response and in Figure 19 in terms of distri-bution profiles of displacements interstory drift index andfloor accelerations Despite the different seismic inputssimilar conclusions of the previous case may be drawn onceagain the BIS with rotational inertia is the best seismic ret-rofitting strategy and outperforms the BIS with supplementaldamping in the reduction of displacements interstory driftsand floor accelerations A conventional low-damping BIS isunacceptable if the conditions specified in (12) should be metfor instance the displacements at the fifth floor exceed 20 cmfor both the earthquakes

Table 3 List of results considering average RMS values of response indicators (Monte Carlo method with 100 artificial samples)

Seismic retrofittingstrategy

Superstructure-related response indicatorsBIS

displacementub(m) middot 10minus2

TMDstroke

ut(m) middot 10minus2Last-floor

displacementus5(m) middot 10minus2

2nd interstorydrift

Δus2(m) middot 10minus4

4th flooracceleration

eurous4(ms2) middot 10minus2

Baseshear

Vb(kN)

Kineticenergy

Ts(kNm)

Strainenergy

Es(Nm)

1 ConventionalBIS(reference solution)

858 1727 8231 2290 3819 18798 792 mdash

2 BIS withrotationalinertia (TMDI)

387 820 4234 1080 988 5025 356 585

(minus548) (minus525) (minus486) (minus531) (minus741) (minus733) (minus551) (minus261)

3 BIS with TMD 561 1102 5395 1460 1818 8449 519 1641(minus347) (minus362) (minus345) (minus364) (minus524) (minus551) (minus346) (+1071)

4 BIS withsupplementaldamping

506 1048 5217 1380 1573 7726 467 mdash

(minus410) (minus393) (minus366) (minus396) (minus588) (minus589) (minus412) mdash


440 1048 5217 1220 1573 7726 400 mdash


Table 4 List of results considering average MAX values of response indicators (Monte Carlo method with 100 artificial samples)




TMDstroke


displacementus5 (m) middot 10minus2

2nd interstorydrift

Δus2 (m) middot 10minus4


eurous4 (ms2) middot 10minus2

Baseshear

Vb (kN)

Kineticenergy

Ts (kNm)

Strainenergy

Es(Nm)

1 Conventional BIS(reference solution) 2367 4823 25832 6340 18205 81951 2181 mdash


1359 3037 18359 3900 7031 32017 1239 1847




1632 3489 2045 4523 9765 42081 1496 mdash



1465 3489 2045 4160 9765 42081 1329 mdash



72 Impact of Tuning Failures due to Uncertainty in theStructural Parameters e observation of real-world ex-amples of BI solutions (see eg [43 45] and the notable case

of the ChristchurchWomensHospital (CWH) in CanterburyNew Zeland [46ndash48] has shown that in reality base-isolatedstructures may not behave as expected during the occurrence

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 50

t (s)

F (k

N)

Inerter force in BIS with rotational inertiaDamping force in BIS with supplemental dampingDamping force in convertional BIS

(a)

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 100

t (s)

F (k

N)


(b)

Figure 16 Time-history for reactive forces relevant to two arbitrary articial accelerograms

0 01 02 03 04 05 06 07Basement

012345

Displacement (m)

Stor

y nu

mbe

r

BIS with rotatiovnal inertiaBIS with supplemental damping

Conventional BIS

Fixed-base buildingreshold value

(a)

BIS with rotatinal inertiaBIS with supplemental damping

Conventional BIS


0

1

2

3

4

5

Stor

y nu

mbe

r

0 01 02 03 04 05 06 07Interstory dri index ()

(b)

0

1

2

3

4

5

0 02 04 06 08 1

Stor

y nu

mbe

r

Floor acceleration (g)


Conventional BIS


(c)

Figure 17 Monte Carlo method with 100 articial samples average maximum distribution of horizontal displacements (a) interstory driftindex (b) and oor acceleration (c) compared to threshold values as per (12)


of seismic events is may be ascribed to the constructionvariations along with the imperfect knowledge of the struc-tural parameters for instance the involved masses (due to thelive loads) and the stiness of the isolators e as-designedand as-implemented scenarios may be quite dierent As anexample in the aforementioned CWH during the Mw58 andMw60 seismic events on December 23 2011 [46] the yieldforce of the LRB isolators was higher than expected thereforethe isolation was quite ineective and the superstructureperformed as a xed-base building to a large extent Actuallythe isolator stiness measured for the Mw58 event was ap-proximately four times higher than the design stiness andvery little damping was recorded unlike the expectations ofthe original design

Based on these observations the assessment of the ef-fectiveness of the proposed BIS +TMDI solution should bemade by incorporating the eect of detuning that is byslightly varying the dynamic properties of natural frequency(thus accounting for the variation in both masses andstiness) and damping ratio of the TMD tuned isolatorsIt seems of valuable importance to scrutinize and quantifythe impact of tuning failure (eects of detuning) on theachieved isolation performance

No practical implementation of the BIS +TMDI strategyin real structures is available so far therefore the investi-gation is here carried out numerically by means of a para-metric analysis In particular the same ve-story RCbuilding shown in Figure 14 is analyzed with the BIS +rotational inertia (TMDI system) e detected tuning pa-rameters of the TMD isolators ωt and ζt are slightly variedfrom their optimal values reported in Table 2 In particularconsidering the previous example of the CWH [46] wherethe actual stiness of the isolators was four times higher thanthe one assumed in the calculation we explore a range ofparameters up the extreme situation in which the naturalfrequency ωt

ktmeffradic

2ωtopt which corresponds toa factor four in the isolator stiness kt Moreover we alsoexplore a similar range of variation for the damping ratio ζt

is is a simplied way to simulate what happened in theCWH [46] due to the discrepancies in the isolator stinessFurthermore this is a simplied way to take into accountthe variability of the isolatorsrsquo mechanical properties duringthe seismic event for example the friction coelaquocient ofthe friction pendulum isolators [49] Relevant results aredepicted in Figures 20 and 21 It can be seen that asa conrmation of the numerical procedure proposed theoptimal tuning parameters lead to the minimization of thelast-oor and the BIS displacements (cf Figure 20) ebase shear and the kinetic energy are also reported in theplots and seem to be minimized by a slightly higher valueof frequency and by a higher damping ratio than the oneassumed for the minimization of the displacements Animportant aspect emerges from this analysis as the tuningparameters depart from their optimal values the structuredisplacements increase and the eectiveness of the iso-lation system decreases accordingly which is quite rea-sonable In particular for a TMD frequency two timeshigher than the optimal one the superstructure dis-placements increase of about 80 and thus the isolationelaquocacy reduces ese results are in line with the con-clusions drawn for the CWH [46] and demonstrate that theisolator stiness is a key parameter in order for the iso-lation to be fully eective A wrong estimation of theTMD frequency may hamper the eectiveness of thistechnology over a broad bandwidth of inputs In thisregard the solution with supplemental damping doesnot suer from this drawback Although the analyzedscenario (isolator stiness four times higher than expectedand natural frequency two times higher than expected) isquite extreme it should be noted that purely providingdamping is not aected by such issues related to detuningeects

73 Critical Discussion and Alternative Systems A variety ofseismic retrotting strategies exist which are obviously not

0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro

Convertional BISBIS with TMDBIS with supplemental dampingBIS with rotational intertia (TMDI)

u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)

Figure 18 Last-oor displacement time-history response of the RC building shown in Figure 14 subject to El Centro (a) and Loma Prieta(b) earthquake ground motion


limited to the few ones discussed in this paper Among thesestrategies we mention the coupling of adjacent buildings bymeans of passive damping devices to reduce the risk ofpounding [50ndash52] and to improve the seismic performanceof the two systems [53ndash55] the introduction of viscousdampers along the height of the building that producedesired levels of interstory drifts while reducing seismicforces [56 57] the interstory isolation by the use of seismicisolators at levels other than the base along the height ofa building [58 59] and the interstory isolation implementedby converting masses already present on the structure intotuned masses according to a nonconventional TMD scheme[38 60] Moreover there are a range of supplementaldampers that do not have a viscous nature for examplebuckling restrained braces yielding fuse systems and theHF2V device based on the lead extrusion technology[61ndash64] to quote just a few In these cases the simplifiedassumption of a linear viscous damping made throughoutthis paper does not apply and one should consider a morecomplicated constitutive behavior which is beyond thescope of the present study Additionally the class of so-

called semi-active devices having variable effective stiffnessandor variable effective damping provides supplementaldamping while keeping the overall base shear limited In thiscontext resettable stiffness devices using electrorheologicaland magnetorheological materials have been increasinglydeveloped [65ndash67] and studied in large-scale experimentalvalidations in an attempt to optimize damping andminimizeresponse by effectively reshaping and customizing thehysteretic loops (see eg [68ndash71]) ampe nonlinearity of thesemodels including valve size mass flow rate and friction hasbeen investigated in experiments and numerical models [72]Other types of nonlinear viscous dampers are the direction-and displacement-dependent (D3) devices proposed in [73]that are entirely passive thus representing more robust andlower cost devices ampese are just a few devices and tech-nologies and the list is far from being exhaustive (seeeg [74 75] for an overview) ampis very long list underlinesthat the present analysis has only focused on a quite limitedset of intervention strategies making some simplifyingassumptions Further investigation is certainly neededto address the problem in a more comprehensive fashion

Conventional BISBIS with rotational inertiaBIS with supplemental dampingFixed-base buildingreshold value

0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)


Interstory dri index ()0 02 04 06

0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5

Interstory dri index ()


Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)

Figure 19 Average maximum distribution of horizontal displacements (a d) interstory drift index (b e) and floor acceleration (c f) forEl Centro and Loma Prieta earthquake ground motions


by extending and generalizing the results here found Nev-ertheless a few advantages of the proposed technique com-bining seismic base isolation with supplemental rotationalinertia over alternative strategies at least those dealt with inthe present analysis may be recognized as follows

(1) e retrotting operations are limited just to theground oor level or to the basement level thus notinterfering with the architectural aspects of thebuilding along its height and the remaining parts ofthe structure do not have to be modied andoraltered (unlike other systems applied to the struc-tural elements directly (see eg [76 77]))

(2) It is well known that the seismic base isolationpermits a strong reduction of forces to the su-perstructure so that the building can be designedto remain in the elastic range Consequentlylimited damage is expected in the superstructurethus avoiding interruption of operational andfunctional aspects of the building while plastic-nonlinear behavior is concentrated at the isolationlevel is consideration stated for the conven-tional BIS also applies to the improved BIS withsupplemental rotational inertia In other wordsduring and after the earthquake the structure canin principle continue to hold its function which isof extreme importance for strategic buildingshaving civil and social duties

(3) As compared to the conventional base isolationscheme the displacements are drastically reducedin the proposed BIS with supplemental rotationalinertia which is essential in existing structureswith limited seismic joints Moreover it has beenfound that also interstory drifts (related to theinternal stress of the frame elements) and oor

accelerations are reduced by the proposed strat-egy much more than employing supplementaldamping

(4) e inerter is a quite compact mechanical device thatcan be designed to provide any desired value ofinertance On the contrary eective vibration re-duction is achieved by the TMD provided that largeamounts of mass are introduced into the systemUnless an architectural function is assigned to suchan additional mass (eg a parking space and utilitiesroom) the feasibility and cost-eectiveness of thisretrotting strategy may be hampered in practicalapplications because of economic reasons

(5) e use of the TMD as a retrotting strategy is alsohindered by the TMD strokes which may be un-acceptably large thus requiring a large spaceclearancein the building in order to accommodate the dis-placement demand of this secondary masssubsystemsometimes even exceeding the maximum admissibledisplacement of the BIS

(6) As compared to alternative retrotting strategiescomprising uid viscous dampers installed along theheight of the building the proposed system canaccommodate large relative displacements withoutsuering from the issues of viscous heating andpotential leaking that challenge the implementationof uid dampers [16]

Nevertheless all the encouraging outcomes arisen fromthis study should be better veried before a practicalimplementation of this system for seismic retrottingpurposes can be accomplished For instance while the as-sumption of linear viscous damping for the superstructure isreasonable it would be advisable to extend this research

1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]

Kinetic energy TsBase shear VbLast-floor displacement us5BIS displacement ub

ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)

Figure 20 Impact of tuning failure due to imperfect knowledge of the structural TMD dynamic parameters eect on four responseindicators


work to incorporate a more appropriate realistic nonlinearbehavior of the isolators thus accounting for their actualinelastic characteristics However it has been demonstratedthat the system performs at its best when low-damping(rubber bearing) isolators are considered therefore theequivalent linear viscous damping idealization dealt with inthis paper could represent a reasonable assumption at leastfor preliminary design purposes On the other hand theauxiliary isolators are medium-to-high damping isolatorswhich implies that a better description of their nonlinearbehavior is recommendedis task is left for future researchwork

8 Concluding Remarks

Existing structures having a limited seismic joint and re-quiring a high level of earthquake protection such asbuilding with strategic importance have been addressed inthis paper To limit the forces in the structure and to keep thefunctional and operational aspects of these buildings duringand after earthquakes the strategy of seismic base isolationhas been assumed as the starting point of a seismic retro-tting process On the other hand the limited seismic jointof several existing structures built in the past requires carefulconsiderations on the displacement demand of the base-isolated structure In this paper two alternative remedies arediscussed and compared the former combining a baseisolation system with supplemental damping and the latter

coupling the base isolation with supplemental rotationalinertia via the use of the TMDI which is a TMDwith inertere combination of the base isolation system with a TMDhas retrieved a special case of the system with the TMDI fora zero value of the inertance Optimal design of the systemand the inuence of the soil characteristics on the best tuningparameters have been dealt with A practical strategy ofimplementation of the proposed system into existingstructures is presented which comprises the use of two setsof isolators namely some conventional isolators with low-damping properties and some auxiliary isolators that aremore exible and equipped with medium-to-high dampingcharacteristics e inerter is connected in between theauxiliary isolators and the ground Time-history analysesfor a simple multistory building subject to both articialaccelerograms and natural earthquake ground motions havebeen performed e basic steps involved in a seismic ret-rotting procedure via the proposed technique are outlinedA variety of response indicators are computed that are usefuland of practical importance for design engineers includingthe base shear interstory drifts oor accelerations kineticenergy and so forth It is found that the BIS with supple-mental rotational inertia is a more eective seismic retro-tting strategy than the BIS with supplemental damping forall the response indicators above mentioned at least for thecases here analyzed Advantages of the proposed techniquesover a few other approaches in the literature have also beencritically discussed but only from a qualitative point of view

12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6

05 1 15 2ωtωt opt[ndash]

ζ tζ t

opt [ndash]

1

05

15

2

(d)

Figure 21 Impact of tuning failure due to imperfect knowledge of the structural TMD dynamic parameters surface and contour plots of thelast-oor displacement (a c) and of the base shear (b d) respectively


Sensitivity analysis and the impact of tuning failures due toimperfect knowledge of the structural parameters (eg theTMD mass and the stiffness of the isolators) have also beendiscussed motivated by the observation of a real-world caseexample of isolation [46]

Despite many simplifying assumptions adopted in thispaper and the simplicity of the structural model analyzedthe authorsrsquo opinion is that the BIS with supplemental ro-tational inertia can be considered as a feasible low-mass andefficient seismic retrofitting strategy of existing structureswith limited seismic joint However before a practicalimplementation can be done prototype testing andor ex-perimental findings are essential to gain a more accurateunderstanding of this system and to to validate the idealizedmodels commonly adopted in the literature

Conflicts of Interest

ampe authors declare that they have no conflicts of interest

Acknowledgments

ampe financial support from the Italian Ministry ofEducation University and Research (PRIN Grant2015TTJN95mdashldquoIdentification and monitoring of complexstructural systemsrdquo) is gratefully acknowledged ampe firstauthor wishes to express his personal gratitude to thisresearch fund and also to the PRIN Grant 2015JW9NJTthrough which a postdoctoral scholarship was awarded

References

[1] F Naeim and J M KellyDesign of Seismic Isolated StructuresFrom gteory to Practice John Wiley amp Sons New York NYUSA 1999

[2] V Zayas S Low and S Mahin ldquoampe FPS earthquake resistingsystemrdquo Report No CBEERC-8701 Earthquake EngineeringResearch Center University of California Berkeley CA USA1987

[3] M D Symans F A Charney A S Whittaker et al ldquoEnergydissipation systems for seismic applications current practiceand recent developmentsrdquo Journal of Structural Engineeringvol 134 no 1 pp 3ndash21 2008

[4] T T Soong and G F Dargush Passive Energy DissipationSystems in Structural Engineering John Wiley amp SonsChichester UK 1997

[5] S A Anagnostopoulos and K V Spiliopoulos ldquoAn in-vestigation of earthquake induced pounding between adjacentbuildingsrdquo Earthquake Engineering amp Structural Dynamicsvol 21 no 4 pp 289ndash302 1992

[6] T H Heaton J F Hall D J Wald and M W HallingldquoResponse of high-rise and base-isolated buildings to a hy-pothetical Mw 70 blind thrust earthquakerdquo Science vol 267no 5195 pp 206ndash211 1995

[7] T Ariga Y Kanno and I Takewaki ldquoResonant behaviour ofbase-isolated high-rise buildings under long-period groundmotionsrdquo Structural Design of Tall and Special Buildingsvol 15 no 3 pp 325ndash338 2006

[8] I Takewaki S Murakami K Fujita S Yoshitomi andM Tsuji ldquoampe 2011 off the Pacific coast of Tohoku earthquakeand response of high-rise buildings under long-period ground

motionsrdquo Soil Dynamics and Earthquake Engineering vol 31no 11 pp 1511ndash1528 2011

[9] J M Kelly ldquoampe role of damping in seismic isolationrdquoEarthquake Engineering amp Structural Dynamics vol 28 no 1pp 3ndash20 1999

[10] J P Den Hartog Mechanical Vibrations McGraw-Hill NewYork NY USA 1934

[11] M C Smith ldquoSynthesis of mechanical networks the inerterrdquoIEEE Transactions on Automatic Control vol 47 no 10pp 1648ndash1662 2002

[12] M Z Q Chen C Papageorgiou F Scheibe F-C Wangand M C Smith ldquoampe missing mechanical circuit elementrdquoIEEE Circuits and Systems Magazine vol 9 no 1 pp 10ndash262009

[13] I F Lazar S A Neild and D J Wagg ldquoUsing an inerter-baseddevice for structural vibration suppressionrdquo EarthquakeEngineering amp Structural Dynamics vol 43 no 8 pp 1129ndash1147 2014

[14] L Marian and A Giaralis ldquoOptimal design of a novel tunedmass-damper-inerter (TMDI) passive vibration controlconfiguration for stochastically support-excited structuralsystemsrdquo Probabilistic Engineering Mechanics vol 38pp 156ndash164 2014

[15] D Pietrosanti M De Angelis and M Basili ldquoOptimal designand performance evaluation of systems with Tuned MassDamper Inerter (TMDI)rdquo Earthquake Engineering amp StructuralDynamics vol 46 no 8 pp 1367ndash1388 2017

[16] N Makris and G Kampas ldquoSeismic protection of structureswith supplemental rotational inertiardquo Journal of EngineeringMechanics vol 142 no 11 p 04016089 2016

[17] J N Yang A Danielians and S C Liu ldquoA seismic hybridcontrol systems for building structuresrdquo Journal of EngineeringMechanics vol 117 no 4 pp 836ndash853 1991

[18] T Taniguchi A Der Kiureghian and M Melkumyan ldquoEffectof tuned mass damper on displacement demand of base-isolated structuresrdquo Engineering Structures vol 30 no 12pp 3478ndash3488 2008

[19] H C Tsai ldquoampe effect of tuned-mass dampers on the seismicresponse of base-isolated structuresrdquo International Journal ofSolids and Structures vol 32 no 8-9 pp 1195ndash1210 1995

[20] P Xiang and A Nishitani ldquoOptimum design for more effectivetuned mass damper system and its application to baseisolatedbuildingsrdquo Structural Control and Health Monitoring vol 21no 1 pp 98ndash114 2014

[21] K Saito K Yogo Y Sugimura S Nakaminami and K ParkldquoApplication of rotary inertia to displacement reduction forvibration control systemrdquo in Proceedings of 13th WorldConference on Earthquake Engineering p 13 Vancouver BCCanada 2004

[22] M Saitoh ldquoOn the performance of gyro-mass devices fordisplacement mitigation in base isolation systemsrdquo StructuralControl and Health Monitoring vol 19 no 2 pp 246ndash2592012

[23] D De Domenico N Impollonia and G Ricciardi ldquoSoil-dependent optimum design of a new passive vibration con-trol system combining seismic base isolation with tunedinerter damperrdquo Soil Dynamics and Earthquake Engineeringvol 105 pp 37ndash53 2018

[24] D De Domenico and G Ricciardi ldquoAn enhanced base iso-lation system equipped with optimal Tuned Mass DamperInerter (TMDI)rdquo Earthquake Engineering amp StructuralDynamics pp 1ndash24 2017

[25] T Hashimoto K Fujita M Tsuji and I Takewaki ldquoIn-novative base-isolated building with large mass-ratio TMD at


basement for greater earthquake resiliencerdquo Future Cities andEnvironment vol 1 no 9 pp 1ndash19 2015

[26] European Standard Eurocode 8 Design of Structures forEarthquake Resistance - Part 1 General Rules Seismic Actionsand Rules for Buildings European Committee for Stand-ardisation Brussels Belgium 2003

[27] J Salvi and E Rizzi ldquoOptimum tuning of Tuned MassDampers for frame structures under earthquake excitationrdquoStructural Control and Health Monitoring vol 22 no 4pp 707ndash725 2015

[28] J B Chen W Liu Y Peng and J Li ldquoStochastic seismicresponse and reliability analysis of base-isolated structuresrdquoJournal of Earthquake Engineering vol 11 no 6 pp 903ndash9242007

[29] M B Priestley ldquoEvolutionary spectra and non-stationaryprocessesrdquo Journal of the Royal Statistical Society Series Bvol 27 no 2 pp 204ndash237 1965

[30] A Giaralis and P D Spanos ldquoDerivation of response spec-trum compatible non-stationary stochastic processes relyingon Monte Carlo-based peak factor estimationrdquo Earthquakesand Structures vol 3 no 3-4 pp 581ndash609 2012

[31] T I Hsu and M C Bernard ldquoA random process for earth-quake simulationrdquo Earthquake Engineering amp StructuralDynamics vol 6 no 4 pp 347ndash362 1978

[32] R W Clough and J Penzien Dynamics of StructuresComputers and Structures Inc Berkeley CA USA 3rdedition 2003

[33] P Castaldo and M Ripani ldquoOptimal design of frictionpendulum system properties for isolated structures consid-ering different soil conditionsrdquo Soil Dynamics and EarthquakeEngineering vol 90 pp 74ndash87 2016

[34] K Kanai ldquoSemi-empirical formula for the seismic charac-teristics of the ground motionrdquo Bulletin of the EarthquakeResearch Institute vol 35 no 2 pp 309ndash325 1957

[35] H Tajimi ldquoA statistical method of determining the maximumresponse of a building structure during an earthquakerdquo inProceedings of the 2nd World Conference on EarthquakeEngineering vol 2 pp 781ndash798 Tokyo Japan 1960

[36] H Buchholdt Structural Dynamics for Engineering ampomasTeldfort London UK 1997

[37] A Der Kiureghian and A Neuenhofer ldquoResponse spectrummethod for multi-support seismic excitationsrdquo EarthquakeEngineering amp Structural Dynamics vol 21 no 8 pp 713ndash740 1992

[38] A Reggio and M De Angelis ldquoOptimal energy-basedseismic design of non-conventional Tuned Mass Damper(TMD) implemented via inter-story isolationrdquo EarthquakeEngineering amp Structural Dynamics vol 44 no 10 pp 1623ndash1642 2015

[39] European Standard Eurocode 8 Design of Structures forEarthquake Resistance - Part 3 Assessment and Retrofitting ofBuildings European Committee for Standardisation BrusselsBelgium 2005

[40] D De Domenico ldquoRC members strengthened with externallybonded FRP plates a FE-based limit analysis approachrdquoComposites Part B Engineering vol 71 pp 159ndash174 2015

[41] A K Chopra Dynamics of Structures Pearson Prentice HallUpper Saddle River NJ USA 4th edition 2012

[42] M Shinozuka and G Deodatis ldquoSimulation of stochasticprocesses by spectral representationrdquo Applied MechanicsReviews vol 44 no 4 pp 191ndash203 1991

[43] T Guo W Xu L Song and L Wei ldquoSeismic-isolation retrofitsof school buildings practice in China after recent devastating

earthquakesrdquo Journal of Performance of Constructed Facilitiesvol 28 no 1 pp 96ndash107 2014

[44] F Sadek B Mohraz A W Taylor and R M Chung ldquoAmethod of estimating the parameters of Tuned Mass Dampersfor seismic applicationsrdquo Earthquake Engineering amp StructuralDynamics vol 26 no 6 pp 617ndash635 1997

[45] N Lakshmanan K Sathish Kumar R Sreekala K MuthumaniJ Guru and N Gopalakrishnan ldquoExperimental investigationson the seismic response of a base-isolated reinforced concreteframe modelrdquo Journal of Performance of Constructed Facilitiesvol 22 no 5 pp 289ndash296 2008

[46] A Kuang A Sridhar J Garven et al ldquoChristchurchWomenrsquosHospital performance analysis of the base-isolation systemduring the series of canterbury earthquakes 2011ndash2012rdquoJournal of Performance of Constructed Facilities vol 30 no 4p 04015096 2015

[47] A Sridhar A Kuang J Garven et al ldquoChristchurchWomenrsquosHospital analysis of measured earthquake data during the2011ndash2012 christchurch earthquakesrdquo Earthquake Spectravol 30 no 1 pp 383ndash400 2014

[48] C Zhou J G Chase GW Rodgers A Kuang S Gutschmidtand C Xu ldquoPerformance evaluation of CWH base isolatedbuilding during twomajor earthquakes in christchurchrdquo Bulletinof the New Zealand Society for Earthquake Engineering vol 48no 4 pp 264ndash273 2015

[49] D De Domenico G Ricciardi and G Benzoni ldquoAnalyticaland finite element investigation on the thermo-mechanicalcoupled response of friction isolators under bidirectionalexcitationrdquo Soil Dynamics and Earthquake Engineeringvol 106 pp 131ndash147 2018

[50] B D Westermo ldquoampe dynamics of interstructural connectionto prevent poundingrdquo Earthquake Engineering amp StructuralDynamics vol 18 no 5 pp 687ndash699 1989

[51] M Barbato and E Tubaldi ldquoA probabilistic performance-based approach for mitigating the seismic pounding riskbetween adjacent buildingsrdquo Earthquake Engineering ampStructural Dynamics vol 42 no 8 pp 1203ndash1219 2013

[52] E Tubaldi ldquoDynamic behavior of adjacent buildings con-nected by linear viscousviscoelastic dampersrdquo StructuralControl and Health Monitoring vol 22 no 8 pp 1086ndash11022015

[53] C C Patel and R S Jangid ldquoDynamic response of identicaladjacent structures connected by viscous damperrdquo StructuralControl and Health Monitoring vol 21 no 2 pp 205ndash2242014

[54] K Kim J Rye and L Chung ldquoSeismic performance ofstructures connected by viscoelastic dampersrdquo EngineeringStructures vol 28 no 2 pp 83ndash195 2006

[55] M Basili and M De Angelis ldquoOptimal passive control ofadjacent structures interconnected with nonlinear hystereticdevicesrdquo Journal of Sound and Vibration vol 301 no 1-2pp 106ndash125 2007

[56] O Lavan ldquoAmethodology for the integrated seismic design ofnonlinear buildings with supplemental dampingrdquo StructuralControl and Health Monitoring vol 22 no 3 pp 484ndash4992014

[57] M Martinez-Rodrigo and M L Romero ldquoAn optimumretrofit strategy for moment resisting frames with nonlinearviscous dampers for seismic applicationsrdquo EngineeringStructures vol 25 no 7 pp 913ndash925 2003

[58] L Keri and L Curtis ldquoAnalysis and design of inter-storyisolation systems with nonlinear devicesrdquo Journal of EarthquakeEngineering vol 14 no 7 pp 1044ndash1062 2010


[59] D Charmpis P Komodromos andM C Phocas ldquoOptimizedearthquake response of multi-storey buildings with seismicisolation at various levelsrdquo Earthquake Engineering ampStructural Dynamics vol 41 pp 2289ndash2310 2012

[60] M De Angelis S Perno and A Reggio ldquoDynamic responseand optimal design of structure with large mass ratio TMDrdquoEarthquake Engineering amp Structural Dynamics vol 41 no 1pp 41ndash60 2012

[61] G W Rodgers J G Chase J B Mander N C Leach andC S Denmead ldquoExperimental development tradeoff analysisand design implementation of high force-to-volume dampingtechnologyrdquo Bulletin of the New Zealand Society for EarthquakeEngineering vol 40 no 2 pp 35ndash48 2007

[62] G W Rodgers K M Solberg J G Chase et al ldquoPerfor-mance of a damage-protected beamndashcolumn subassemblyutilizing external HF2V energy dissipation devicesrdquo EarthquakeEngineering amp Structural Dynamics vol 37 no 13 pp 1549ndash1564 2008

[63] T Bacht J G Chase G MacRae et al ldquoHF2V dissipatoreffects on the performance of a 3 story moment framerdquoJournal of Constructional Steel Research vol 67 no 12pp 1843ndash1849 2011

[64] J C Golondrino J G Chase G W Rodgers G A MacRaeand C G Clifton ldquoVelocity effects on the behaviour of high-force-to-volume lead dampers (HF2V) using different shaftconfigurationsrdquo in Proceedings of the 15th World Conferenceon Earthquake Engineering Lisboa Portugal September 2012

[65] J E Bobrow F Jabbari and K ampai ldquoAn active truss elementand control law for vibration suppressionrdquo Smart Materialsand Structures vol 4 no 4 pp 264ndash269 1995

[66] F Jabbari and J E Bobrow ldquoVibration suppression withresettable devicerdquo Journal of Engineering Mechanics vol 128no 9 pp 916ndash924 2002

[67] N K Hazaveh J G Chase G W Rodgers and S PampaninldquoSmart semi-active MR damper to control the structuralresponserdquo Bulletin of the New Zealand Society for EarthquakeEngineering vol 48 no 4 pp 235ndash245 2015

[68] J G Chase K J Mulligan A Gue et al ldquoRe-shaping hys-teretic behaviour using semi-active resettable devicedampersrdquo Engineering Structures vol 28 no 10 pp 1418ndash1429 2006

[69] GW Rodgers J B Mander J Geoffrey Chase K J MulliganB L Deam and A Carr ldquoRe-shaping hysteretic behav-iourmdashspectral analysis and design equations for semi-activestructuresrdquo Earthquake Engineering amp Structural Dynamicsvol 36 no 1 pp 77ndash100 2007

[70] K J Mulligan J G Chase J B Mander et al ldquoExperimentalvalidation of semi-active resetable actuators in a⅕th scale teststructurerdquo Earthquake Engineering amp Structural Dynamicsvol 38 no 4 pp 517ndash536 2009

[71] N K Hazaveh G W Rodgers J G Chase and S PampaninldquoReshaping structural hysteresis response with semi-activeviscous dampingrdquo Bulletin of Earthquake Engineering vol 15no 4 pp 1789ndash1806 2017

[72] K J Mulligan J G Chase J B Mander G W Rodgers andR B Elliott ldquoNonlinear models and validation for resetabledevice design and enhanced force capacityrdquo StructuralControl and Health Monitoring vol 17 no 3 pp 301ndash3162010

[73] N K Hazaveh G W Rodgers J G Chase and S PampaninldquoExperimental test and validation of a direction- anddisplacement-dependent viscous damperrdquo Journal of EngineeringMechanics vol 143 no 11 p 04017132 2017

[74] T T Soong and M C Costantinou Passive and ActiveStructural Vibration Control in Civil Engineering Springer-Verlag Vienna Austria 2014

[75] G W Housner L A Bergman T K Caughey et alldquoStructural control past present and futurerdquo Journal ofEngineering Mechanics vol 123 no 9 pp 897ndash971 1997

[76] D De Domenico P Fuschi S Pardo and A A PisanoldquoStrengthening of steel-reinforced concrete structural ele-ments by externally bonded FRP sheets and evaluation of theirload carrying capacityrdquo Composite Structures vol 118pp 377ndash384 2014

[77] D De Domenico A A Pisano and P Fuschi ldquoLimit analysison FRP-strengthened RC membersrdquo Frattura ed IntegritaStrutturale vol 8 no 29 pp 209ndash221 2014


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(eg waterworks gas fittings and electrical conduits) Inmost cases this implies a complete refurbishment of theexisting more rigid pipelines which significantly increasesthe overall retrofitting costs In addition an adequate sep-aration distance between adjacent buildings also calledseismic joint must be present in order to prevent mutualcollisions or structural pounding [5] ampe latter aspect maylimit the base isolation applications in those cases involvinga limited space between adjacent buildings as the actualseismic joint may easily be exceeded by the design dis-placement of the BIS amperefore the goal is to find a seismicprotection strategy such that the superstructure will expe-rience little damage but at the same time the overall dis-placement of the structure remains limited to withina reasonably acceptable threshold thus not exceeding theseismic joint Another problem that is often encountered inseismic base isolation is the vulnerability to long-periodground motions that might severely increase the lateraldisplacements of the isolators and cause long-lasting vi-brations due to the resonance effects [6] in a similar fashionto high-rise flexible-frame buildings [7 8]

ampese shortcomings have motivated the developmentof improved versions of the conventional base isolationscheme ampe most straightforward remedy for reducing theBIS displacement is to increase the isolation damping or toprovide supplemental damping Although this strategy doesreduce the excessively large displacements in the BIS it mayincrease the interstory drifts and floor accelerations in thesuperstructure [9] In addition to disturbing occupants thismay be an issue for nonstructural elements and equipmentthat could be of valuable importance in the above mentionedstrategic buildings (eg control centers real-time acquisi-tion data centers and so on) As an alternative a hybridcontrol strategy combining the conventional base isolationsystem with supplemental rotational inertia is proposed inthis paper In particular the BIS is coupled with the so-calledtuned-mass-damper-inerter (TMDI) ampe latter system byanalogy with the tuned mass damper (TMD) [10] consists ofmass spring and damper elements that are installed in serieswith a novel type of device the inerter [11] Details of thissystem will be discussed below

ampis paper compares the above two alternative strategiesfor the seismic retrofitting of existing buildings namelyseismic base isolation with supplemental damping versusseismic base isolation with supplemental rotational inertiaOptimal tuning parameters of the TMDI are detected withina probabilistic framework by considering the stochasticnature of earthquake ground motions and solving a non-linear optimization problem ampe earthquake ground mo-tion is modelled as a Gaussian process in the frequencydomain through the use of the power spectral density (PSD)function ampe influence of soil characteristics is investigatedby introducing three PSD functions representatives of firmmedium and soft soil conditions Based on the optimalparameters found a possible implementation scheme withregard to existing structures is proposed Some numericalapplications demonstrate advantages and disadvantages ofthe two vibration control strategies with regard to thestructural control of existing structures not only in terms of

displacement but also in terms of transmitted forces andother response indicators such as the base shear theinterstory drifts and the floor accelerations in order toevaluate the overall performance of these seismic protectionsystems

2 Inerter and Tuned-Mass-Damper-Inerter(TMDI)

ampe inerter element was introduced by Smith [11] in 2002 tocomplete the force-current analogy between mechanical andelectrical networks In particular the inerter has beenproposed as the mechanical counterpart of the capacitorconcept in electrical systems If u1 and u2 are the dis-placement coordinates of the two terminals connected by theinerter the following relationship holds for the ideal linearinerter

F b eurou1 minus eurou2( 1113857 (1)

where the constant of proportionality b is called inertanceand has dimensions of mass thereby it has been sometimestermed ldquoapparent massrdquo From (1) it is shown that theinternal force of the inerter is proportional to the relativeacceleration of its two terminals similarly to the damper andspring elements whose internal force is proportional to therelative velocity and displacement respectively

As schematically shown in Figure 1 the inerter can berealized through a two-terminal device that consists ofa combined arrangement of a rack pinions gears anda flywheel In this figure mf is the mass of the flywheel ri

and rpi denote the radius of gears and pinions respectivelyrf is the radius of the flywheel and rpf indicates the radius ofthe flywheel pinion Linear movement of the rack generatesrotational movement in gears and flywheel and the iner-tance of this system can be expressed as

b mf

r2f

r2pf1113945

n

i1

r2ir2pi

⎛⎝ ⎞⎠ (2)

where n is the number of gears amperefore this system isbased on the concept of rotational inertia Alternative re-alizations involve a rotary ball screw and a flywheel toconvert axial movement into rotary displacements ampeinerter has also been employed in the automotive sectorunder the name of J-damper for Formula 1 racing carsuspensions [12] By adjusting the gearing ratios or simplyintroducing additional gears it is possible to attain very highvalues of the inertance b without implying a large amount ofphysical mass mf In principle any desired value of b can beobtained with a device of reasonably compact form Suchmass amplification effect is the key feature of this system andmakes it appealing for vibration control purposes it has beendemonstrated that the apparent mass can be designed to beorders of magnitude (up to 200 times) higher than thephysical mass of the device ampis peculiarity has beenexploited in the context of enhancing the performance oftuned mass dampers (TMDs) In particular as sketched inFigure 2 the TMDI consists of an enhanced version of TMD(of mass mt spring stiffness kt and viscous damping ct)







Terminal 1

u1 u2

Rotarymovement

Gear

r1

r2

rfrn

rpn mfrpf

rp2

rp1

Flywheel

Pinion



Inerter1

1 2

2

bt

ct

kt

mt

m1u1

ut

kt

ct

F = btuumlg

uumlg






with

M 1 1 0

1 1 + μb 0

0 0 μt + βt

C 2ζsωs 0 0


K ω2s 0 0

0 ω2bμb + ω2

tμet minusω2tμet

0 minusω2tμet ω2

tμet

τ 1

1 + μbμt

u usr(t)ub(t)ut(t)

(4)


mtmb

cs

ms

ct

kt

ks

kb cb ug

ut

ub

us

usr

uumlg

large mass


structural SDOF

TMD

(a)

mt

mbbt

ms

kt

ks

ug

ub

us

ut

usr

uumlg

cs

kb cb

ct

F = btuumlg


Structural SDOF

TMDI1

1

2

2

Inerter

(b)



ωs

ks

ms

1113971

ζs cs

2msωs

ωb

kb

mb

1113971

ζb cb

2mbωb

ωt

kt

mt + bt

1113971

ζt ct

2 mt + bt( 1113857ωt

μb mb

ms

μt mt

ms

βt bt

ms

μet mt + bt

ms

met

ms

(5)












H



uslf

ub

(a)



uslf

ub

H

(b)




Sensitive equipment


uslf

ub

H

(c)










2gω

2

ω2g minusω2( )

2 + 4ζ2gω2gω2

ω4

ω2f minusω2( )

2+ 4ζ2fω2

fω2Sw

(8)


Sw 0141ζg eurou

2g0








030

002

520

004

43

006

10 210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(a)

030

004

20

008

54

012

10 3210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(b)

030

012

20

024

54

036

10 3210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(c)




minx





2us0




0 01 02 03 04 05 060

02040608

1

βt

μt = 001μt = 01μt = 04


σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

βt

μt = 001μt = 01μt = 04


ν t op

t=ϖ t

opt

ϖb

(b)

0 01 02 03 04 05 060

01

02

03

04

βt

μt = 001μt = 01μt = 04


ζ t op

t

(c)


0 01 02 03 04 05 060

02040608

1

βt

μt = 001μt = 01μt = 04


σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

βt

μt = 001μt = 01μt = 04


ν t op

t=ϖ t

opt

ϖb

(b)

0 01 02 03 04 05 060

01

02

03

04

βt

μt = 001μt = 01μt = 04


opt

(c)







0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04

So soil conditions

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04

So soil conditions

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04

So soil conditions

βt

(c)


0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04


βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04


βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04


βt

(c)






2s tot] 4ζ2sω

2sσ

2_usr+ ω4





0 01 02 03 04 05 060

02040608

1



ζb = 03 (LDRB)

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06025

03

035

04

ν t op

t=ϖ t

opt

ϖb



ζb = 03 (LDRB)

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t



ζb = 03 (LDRB)

βt

(c)


0 01 02 03 04 05 060

02

04

06

081

σ2uuml s t

otσ

2 uuml s0 to

t

βt



(a)

001

01

10

1

50

0 01 02 03 04 05 06βt

Stro

ke =

σ2 u tσ

2 u b0




ζb = 03

MediumSoWhite-noise

Firm

(b)















ms

csks

kt ctkb cb

mb

mt

bt

uumlg t












EXIT





Yes

No




Seismicretrofitting





with s H

100 016 m


030⟶Δhlt 00096 m





radicsumNminus1

i0

2S(iΔω)Δωradic





H = 32 hc = 06

hc = 06

hc = 06

hc = 05

hc = 04

hb = 06

hb = 06

hb = 07

hb = 07

hb = 07

h b

h c

hc

H = 32

H = 32

H = 32

H = 32

Beamsection

03

0303

kb cbkt ct

bt

L = 45 L = 45 L = 45

Columnsection

L = 45 L = 45




1 + μminus1b




sic2sidsi the














0acc 50

5 10 15 20 25 30ndash04

ndash02

0

02

04u s

5 (m

)

t (s)


(a)

acc 1000 5 10 15 20 25 30

ndash025

ndash015

ndash005

005

015

025

u s5

(m)

t (s)


(b)

acc 500 5 10 15 20 25 30

ndash06

ndash03

0

03

06

u t (m

)

t (s)


(c)

0 5 10 15 20 25 30ndash04

ndash02

0

02

04

u t (m

)

t (s)


acc 100

(d)










TMDstroke



2nd interstorydrift




Baseshear

Vb(kN)

Kineticenergy

Ts(kNm)

Strainenergy

Es(Nm)


858 1727 8231 2290 3819 18798 792 mdash


387 820 4234 1080 988 5025 356 585




506 1048 5217 1380 1573 7726 467 mdash



440 1048 5217 1220 1573 7726 400 mdash






TMDstroke



2nd interstorydrift




Baseshear

Vb (kN)

Kineticenergy

Ts (kNm)

Strainenergy

Es(Nm)



1359 3037 18359 3900 7031 32017 1239 1847




1632 3489 2045 4523 9765 42081 1496 mdash



1465 3489 2045 4160 9765 42081 1329 mdash





0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 50

t (s)

F (k

N)


(a)

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 100

t (s)

F (k

N)


(b)


0 01 02 03 04 05 06 07Basement

012345

Displacement (m)

Stor

y nu

mbe

r


Conventional BIS


(a)


Conventional BIS


0

1

2

3

4

5

Stor

y nu

mbe

r


(b)

0

1

2

3

4

5

0 02 04 06 08 1

Stor

y nu

mbe

r



Conventional BIS


(c)






ktmeffradic




0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro


u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)






0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







Terminal 1

u1 u2

Rotarymovement

Gear

r1

r2

rfrn

rpn mfrpf

rp2

rp1

Flywheel

Pinion



Inerter1

1 2

2

bt

ct

kt

mt

m1u1

ut

kt

ct

F = btuumlg

uumlg






with

M 1 1 0

1 1 + μb 0

0 0 μt + βt

C 2ζsωs 0 0


K ω2s 0 0

0 ω2bμb + ω2

tμet minusω2tμet

0 minusω2tμet ω2

tμet

τ 1

1 + μbμt

u usr(t)ub(t)ut(t)

(4)


mtmb

cs

ms

ct

kt

ks

kb cb ug

ut

ub

us

usr

uumlg

large mass


structural SDOF

TMD

(a)

mt

mbbt

ms

kt

ks

ug

ub

us

ut

usr

uumlg

cs

kb cb

ct

F = btuumlg


Structural SDOF

TMDI1

1

2

2

Inerter

(b)



ωs

ks

ms

1113971

ζs cs

2msωs

ωb

kb

mb

1113971

ζb cb

2mbωb

ωt

kt

mt + bt

1113971

ζt ct

2 mt + bt( 1113857ωt

μb mb

ms

μt mt

ms

βt bt

ms

μet mt + bt

ms

met

ms

(5)












H



uslf

ub

(a)



uslf

ub

H

(b)




Sensitive equipment


uslf

ub

H

(c)










2gω

2

ω2g minusω2( )

2 + 4ζ2gω2gω2

ω4

ω2f minusω2( )

2+ 4ζ2fω2

fω2Sw

(8)


Sw 0141ζg eurou

2g0








030

002

520

004

43

006

10 210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(a)

030

004

20

008

54

012

10 3210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(b)

030

012

20

024

54

036

10 3210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(c)




minx





2us0




0 01 02 03 04 05 060

02040608

1

βt

μt = 001μt = 01μt = 04


σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

βt

μt = 001μt = 01μt = 04


ν t op

t=ϖ t

opt

ϖb

(b)

0 01 02 03 04 05 060

01

02

03

04

βt

μt = 001μt = 01μt = 04


ζ t op

t

(c)


0 01 02 03 04 05 060

02040608

1

βt

μt = 001μt = 01μt = 04


σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

βt

μt = 001μt = 01μt = 04


ν t op

t=ϖ t

opt

ϖb

(b)

0 01 02 03 04 05 060

01

02

03

04

βt

μt = 001μt = 01μt = 04


opt

(c)







0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04

So soil conditions

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04

So soil conditions

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04

So soil conditions

βt

(c)


0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04


βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04


βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04


βt

(c)






2s tot] 4ζ2sω

2sσ

2_usr+ ω4





0 01 02 03 04 05 060

02040608

1



ζb = 03 (LDRB)

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06025

03

035

04

ν t op

t=ϖ t

opt

ϖb



ζb = 03 (LDRB)

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t



ζb = 03 (LDRB)

βt

(c)


0 01 02 03 04 05 060

02

04

06

081

σ2uuml s t

otσ

2 uuml s0 to

t

βt



(a)

001

01

10

1

50

0 01 02 03 04 05 06βt

Stro

ke =

σ2 u tσ

2 u b0




ζb = 03

MediumSoWhite-noise

Firm

(b)















ms

csks

kt ctkb cb

mb

mt

bt

uumlg t












EXIT





Yes

No




Seismicretrofitting





with s H

100 016 m


030⟶Δhlt 00096 m





radicsumNminus1

i0

2S(iΔω)Δωradic





H = 32 hc = 06

hc = 06

hc = 06

hc = 05

hc = 04

hb = 06

hb = 06

hb = 07

hb = 07

hb = 07

h b

h c

hc

H = 32

H = 32

H = 32

H = 32

Beamsection

03

0303

kb cbkt ct

bt

L = 45 L = 45 L = 45

Columnsection

L = 45 L = 45




1 + μminus1b




sic2sidsi the














0acc 50

5 10 15 20 25 30ndash04

ndash02

0

02

04u s

5 (m

)

t (s)


(a)

acc 1000 5 10 15 20 25 30

ndash025

ndash015

ndash005

005

015

025

u s5

(m)

t (s)


(b)

acc 500 5 10 15 20 25 30

ndash06

ndash03

0

03

06

u t (m

)

t (s)


(c)

0 5 10 15 20 25 30ndash04

ndash02

0

02

04

u t (m

)

t (s)


acc 100

(d)










TMDstroke



2nd interstorydrift




Baseshear

Vb(kN)

Kineticenergy

Ts(kNm)

Strainenergy

Es(Nm)


858 1727 8231 2290 3819 18798 792 mdash


387 820 4234 1080 988 5025 356 585




506 1048 5217 1380 1573 7726 467 mdash



440 1048 5217 1220 1573 7726 400 mdash






TMDstroke



2nd interstorydrift




Baseshear

Vb (kN)

Kineticenergy

Ts (kNm)

Strainenergy

Es(Nm)



1359 3037 18359 3900 7031 32017 1239 1847




1632 3489 2045 4523 9765 42081 1496 mdash



1465 3489 2045 4160 9765 42081 1329 mdash





0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 50

t (s)

F (k

N)


(a)

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 100

t (s)

F (k

N)


(b)


0 01 02 03 04 05 06 07Basement

012345

Displacement (m)

Stor

y nu

mbe

r


Conventional BIS


(a)


Conventional BIS


0

1

2

3

4

5

Stor

y nu

mbe

r


(b)

0

1

2

3

4

5

0 02 04 06 08 1

Stor

y nu

mbe

r



Conventional BIS


(c)






ktmeffradic




0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro


u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)






0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





with

M 1 1 0

1 1 + μb 0

0 0 μt + βt

C 2ζsωs 0 0


K ω2s 0 0

0 ω2bμb + ω2

tμet minusω2tμet

0 minusω2tμet ω2

tμet

τ 1

1 + μbμt

u usr(t)ub(t)ut(t)

(4)


mtmb

cs

ms

ct

kt

ks

kb cb ug

ut

ub

us

usr

uumlg

large mass


structural SDOF

TMD

(a)

mt

mbbt

ms

kt

ks

ug

ub

us

ut

usr

uumlg

cs

kb cb

ct

F = btuumlg


Structural SDOF

TMDI1

1

2

2

Inerter

(b)



ωs

ks

ms

1113971

ζs cs

2msωs

ωb

kb

mb

1113971

ζb cb

2mbωb

ωt

kt

mt + bt

1113971

ζt ct

2 mt + bt( 1113857ωt

μb mb

ms

μt mt

ms

βt bt

ms

μet mt + bt

ms

met

ms

(5)












H



uslf

ub

(a)



uslf

ub

H

(b)




Sensitive equipment


uslf

ub

H

(c)










2gω

2

ω2g minusω2( )

2 + 4ζ2gω2gω2

ω4

ω2f minusω2( )

2+ 4ζ2fω2

fω2Sw

(8)


Sw 0141ζg eurou

2g0








030

002

520

004

43

006

10 210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(a)

030

004

20

008

54

012

10 3210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(b)

030

012

20

024

54

036

10 3210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(c)




minx





2us0




0 01 02 03 04 05 060

02040608

1

βt

μt = 001μt = 01μt = 04


σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

βt

μt = 001μt = 01μt = 04


ν t op

t=ϖ t

opt

ϖb

(b)

0 01 02 03 04 05 060

01

02

03

04

βt

μt = 001μt = 01μt = 04


ζ t op

t

(c)


0 01 02 03 04 05 060

02040608

1

βt

μt = 001μt = 01μt = 04


σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

βt

μt = 001μt = 01μt = 04


ν t op

t=ϖ t

opt

ϖb

(b)

0 01 02 03 04 05 060

01

02

03

04

βt

μt = 001μt = 01μt = 04


opt

(c)







0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04

So soil conditions

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04

So soil conditions

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04

So soil conditions

βt

(c)


0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04


βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04


βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04


βt

(c)






2s tot] 4ζ2sω

2sσ

2_usr+ ω4





0 01 02 03 04 05 060

02040608

1



ζb = 03 (LDRB)

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06025

03

035

04

ν t op

t=ϖ t

opt

ϖb



ζb = 03 (LDRB)

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t



ζb = 03 (LDRB)

βt

(c)


0 01 02 03 04 05 060

02

04

06

081

σ2uuml s t

otσ

2 uuml s0 to

t

βt



(a)

001

01

10

1

50

0 01 02 03 04 05 06βt

Stro

ke =

σ2 u tσ

2 u b0




ζb = 03

MediumSoWhite-noise

Firm

(b)















ms

csks

kt ctkb cb

mb

mt

bt

uumlg t












EXIT





Yes

No




Seismicretrofitting





with s H

100 016 m


030⟶Δhlt 00096 m





radicsumNminus1

i0

2S(iΔω)Δωradic





H = 32 hc = 06

hc = 06

hc = 06

hc = 05

hc = 04

hb = 06

hb = 06

hb = 07

hb = 07

hb = 07

h b

h c

hc

H = 32

H = 32

H = 32

H = 32

Beamsection

03

0303

kb cbkt ct

bt

L = 45 L = 45 L = 45

Columnsection

L = 45 L = 45




1 + μminus1b




sic2sidsi the














0acc 50

5 10 15 20 25 30ndash04

ndash02

0

02

04u s

5 (m

)

t (s)


(a)

acc 1000 5 10 15 20 25 30

ndash025

ndash015

ndash005

005

015

025

u s5

(m)

t (s)


(b)

acc 500 5 10 15 20 25 30

ndash06

ndash03

0

03

06

u t (m

)

t (s)


(c)

0 5 10 15 20 25 30ndash04

ndash02

0

02

04

u t (m

)

t (s)


acc 100

(d)










TMDstroke



2nd interstorydrift




Baseshear

Vb(kN)

Kineticenergy

Ts(kNm)

Strainenergy

Es(Nm)


858 1727 8231 2290 3819 18798 792 mdash


387 820 4234 1080 988 5025 356 585




506 1048 5217 1380 1573 7726 467 mdash



440 1048 5217 1220 1573 7726 400 mdash






TMDstroke



2nd interstorydrift




Baseshear

Vb (kN)

Kineticenergy

Ts (kNm)

Strainenergy

Es(Nm)



1359 3037 18359 3900 7031 32017 1239 1847




1632 3489 2045 4523 9765 42081 1496 mdash



1465 3489 2045 4160 9765 42081 1329 mdash





0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 50

t (s)

F (k

N)


(a)

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 100

t (s)

F (k

N)


(b)


0 01 02 03 04 05 06 07Basement

012345

Displacement (m)

Stor

y nu

mbe

r


Conventional BIS


(a)


Conventional BIS


0

1

2

3

4

5

Stor

y nu

mbe

r


(b)

0

1

2

3

4

5

0 02 04 06 08 1

Stor

y nu

mbe

r



Conventional BIS


(c)






ktmeffradic




0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro


u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)






0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


ωs

ks

ms

1113971

ζs cs

2msωs

ωb

kb

mb

1113971

ζb cb

2mbωb

ωt

kt

mt + bt

1113971

ζt ct

2 mt + bt( 1113857ωt

μb mb

ms

μt mt

ms

βt bt

ms

μet mt + bt

ms

met

ms

(5)












H



uslf

ub

(a)



uslf

ub

H

(b)




Sensitive equipment


uslf

ub

H

(c)










2gω

2

ω2g minusω2( )

2 + 4ζ2gω2gω2

ω4

ω2f minusω2( )

2+ 4ζ2fω2

fω2Sw

(8)


Sw 0141ζg eurou

2g0








030

002

520

004

43

006

10 210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(a)

030

004

20

008

54

012

10 3210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(b)

030

012

20

024

54

036

10 3210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(c)




minx





2us0




0 01 02 03 04 05 060

02040608

1

βt

μt = 001μt = 01μt = 04


σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

βt

μt = 001μt = 01μt = 04


ν t op

t=ϖ t

opt

ϖb

(b)

0 01 02 03 04 05 060

01

02

03

04

βt

μt = 001μt = 01μt = 04


ζ t op

t

(c)


0 01 02 03 04 05 060

02040608

1

βt

μt = 001μt = 01μt = 04


σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

βt

μt = 001μt = 01μt = 04


ν t op

t=ϖ t

opt

ϖb

(b)

0 01 02 03 04 05 060

01

02

03

04

βt

μt = 001μt = 01μt = 04


opt

(c)







0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04

So soil conditions

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04

So soil conditions

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04

So soil conditions

βt

(c)


0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04


βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04


βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04


βt

(c)






2s tot] 4ζ2sω

2sσ

2_usr+ ω4





0 01 02 03 04 05 060

02040608

1



ζb = 03 (LDRB)

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06025

03

035

04

ν t op

t=ϖ t

opt

ϖb



ζb = 03 (LDRB)

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t



ζb = 03 (LDRB)

βt

(c)


0 01 02 03 04 05 060

02

04

06

081

σ2uuml s t

otσ

2 uuml s0 to

t

βt



(a)

001

01

10

1

50

0 01 02 03 04 05 06βt

Stro

ke =

σ2 u tσ

2 u b0




ζb = 03

MediumSoWhite-noise

Firm

(b)















ms

csks

kt ctkb cb

mb

mt

bt

uumlg t












EXIT





Yes

No




Seismicretrofitting





with s H

100 016 m


030⟶Δhlt 00096 m





radicsumNminus1

i0

2S(iΔω)Δωradic





H = 32 hc = 06

hc = 06

hc = 06

hc = 05

hc = 04

hb = 06

hb = 06

hb = 07

hb = 07

hb = 07

h b

h c

hc

H = 32

H = 32

H = 32

H = 32

Beamsection

03

0303

kb cbkt ct

bt

L = 45 L = 45 L = 45

Columnsection

L = 45 L = 45




1 + μminus1b




sic2sidsi the














0acc 50

5 10 15 20 25 30ndash04

ndash02

0

02

04u s

5 (m

)

t (s)


(a)

acc 1000 5 10 15 20 25 30

ndash025

ndash015

ndash005

005

015

025

u s5

(m)

t (s)


(b)

acc 500 5 10 15 20 25 30

ndash06

ndash03

0

03

06

u t (m

)

t (s)


(c)

0 5 10 15 20 25 30ndash04

ndash02

0

02

04

u t (m

)

t (s)


acc 100

(d)










TMDstroke



2nd interstorydrift




Baseshear

Vb(kN)

Kineticenergy

Ts(kNm)

Strainenergy

Es(Nm)


858 1727 8231 2290 3819 18798 792 mdash


387 820 4234 1080 988 5025 356 585




506 1048 5217 1380 1573 7726 467 mdash



440 1048 5217 1220 1573 7726 400 mdash






TMDstroke



2nd interstorydrift




Baseshear

Vb (kN)

Kineticenergy

Ts (kNm)

Strainenergy

Es(Nm)



1359 3037 18359 3900 7031 32017 1239 1847




1632 3489 2045 4523 9765 42081 1496 mdash



1465 3489 2045 4160 9765 42081 1329 mdash





0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 50

t (s)

F (k

N)


(a)

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 100

t (s)

F (k

N)


(b)


0 01 02 03 04 05 06 07Basement

012345

Displacement (m)

Stor

y nu

mbe

r


Conventional BIS


(a)


Conventional BIS


0

1

2

3

4

5

Stor

y nu

mbe

r


(b)

0

1

2

3

4

5

0 02 04 06 08 1

Stor

y nu

mbe

r



Conventional BIS


(c)






ktmeffradic




0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro


u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)






0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







H



uslf

ub

(a)



uslf

ub

H

(b)




Sensitive equipment


uslf

ub

H

(c)










2gω

2

ω2g minusω2( )

2 + 4ζ2gω2gω2

ω4

ω2f minusω2( )

2+ 4ζ2fω2

fω2Sw

(8)


Sw 0141ζg eurou

2g0








030

002

520

004

43

006

10 210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(a)

030

004

20

008

54

012

10 3210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(b)

030

012

20

024

54

036

10 3210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(c)




minx





2us0




0 01 02 03 04 05 060

02040608

1

βt

μt = 001μt = 01μt = 04


σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

βt

μt = 001μt = 01μt = 04


ν t op

t=ϖ t

opt

ϖb

(b)

0 01 02 03 04 05 060

01

02

03

04

βt

μt = 001μt = 01μt = 04


ζ t op

t

(c)


0 01 02 03 04 05 060

02040608

1

βt

μt = 001μt = 01μt = 04


σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

βt

μt = 001μt = 01μt = 04


ν t op

t=ϖ t

opt

ϖb

(b)

0 01 02 03 04 05 060

01

02

03

04

βt

μt = 001μt = 01μt = 04


opt

(c)







0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04

So soil conditions

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04

So soil conditions

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04

So soil conditions

βt

(c)


0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04


βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04


βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04


βt

(c)






2s tot] 4ζ2sω

2sσ

2_usr+ ω4





0 01 02 03 04 05 060

02040608

1



ζb = 03 (LDRB)

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06025

03

035

04

ν t op

t=ϖ t

opt

ϖb



ζb = 03 (LDRB)

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t



ζb = 03 (LDRB)

βt

(c)


0 01 02 03 04 05 060

02

04

06

081

σ2uuml s t

otσ

2 uuml s0 to

t

βt



(a)

001

01

10

1

50

0 01 02 03 04 05 06βt

Stro

ke =

σ2 u tσ

2 u b0




ζb = 03

MediumSoWhite-noise

Firm

(b)















ms

csks

kt ctkb cb

mb

mt

bt

uumlg t












EXIT





Yes

No




Seismicretrofitting





with s H

100 016 m


030⟶Δhlt 00096 m





radicsumNminus1

i0

2S(iΔω)Δωradic





H = 32 hc = 06

hc = 06

hc = 06

hc = 05

hc = 04

hb = 06

hb = 06

hb = 07

hb = 07

hb = 07

h b

h c

hc

H = 32

H = 32

H = 32

H = 32

Beamsection

03

0303

kb cbkt ct

bt

L = 45 L = 45 L = 45

Columnsection

L = 45 L = 45




1 + μminus1b




sic2sidsi the














0acc 50

5 10 15 20 25 30ndash04

ndash02

0

02

04u s

5 (m

)

t (s)


(a)

acc 1000 5 10 15 20 25 30

ndash025

ndash015

ndash005

005

015

025

u s5

(m)

t (s)


(b)

acc 500 5 10 15 20 25 30

ndash06

ndash03

0

03

06

u t (m

)

t (s)


(c)

0 5 10 15 20 25 30ndash04

ndash02

0

02

04

u t (m

)

t (s)


acc 100

(d)










TMDstroke



2nd interstorydrift




Baseshear

Vb(kN)

Kineticenergy

Ts(kNm)

Strainenergy

Es(Nm)


858 1727 8231 2290 3819 18798 792 mdash


387 820 4234 1080 988 5025 356 585




506 1048 5217 1380 1573 7726 467 mdash



440 1048 5217 1220 1573 7726 400 mdash






TMDstroke



2nd interstorydrift




Baseshear

Vb (kN)

Kineticenergy

Ts (kNm)

Strainenergy

Es(Nm)



1359 3037 18359 3900 7031 32017 1239 1847




1632 3489 2045 4523 9765 42081 1496 mdash



1465 3489 2045 4160 9765 42081 1329 mdash





0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 50

t (s)

F (k

N)


(a)

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 100

t (s)

F (k

N)


(b)


0 01 02 03 04 05 06 07Basement

012345

Displacement (m)

Stor

y nu

mbe

r


Conventional BIS


(a)


Conventional BIS


0

1

2

3

4

5

Stor

y nu

mbe

r


(b)

0

1

2

3

4

5

0 02 04 06 08 1

Stor

y nu

mbe

r



Conventional BIS


(c)






ktmeffradic




0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro


u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)






0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









2gω

2

ω2g minusω2( )

2 + 4ζ2gω2gω2

ω4

ω2f minusω2( )

2+ 4ζ2fω2

fω2Sw

(8)


Sw 0141ζg eurou

2g0








030

002

520

004

43

006

10 210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(a)

030

004

20

008

54

012

10 3210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(b)

030

012

20

024

54

036

10 3210 0t (s)

Suumlg(ϖ t) (m2s3)

ϖ2π (Hz)

(c)




minx





2us0




0 01 02 03 04 05 060

02040608

1

βt

μt = 001μt = 01μt = 04


σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

βt

μt = 001μt = 01μt = 04


ν t op

t=ϖ t

opt

ϖb

(b)

0 01 02 03 04 05 060

01

02

03

04

βt

μt = 001μt = 01μt = 04


ζ t op

t

(c)


0 01 02 03 04 05 060

02040608

1

βt

μt = 001μt = 01μt = 04


σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

βt

μt = 001μt = 01μt = 04


ν t op

t=ϖ t

opt

ϖb

(b)

0 01 02 03 04 05 060

01

02

03

04

βt

μt = 001μt = 01μt = 04


opt

(c)







0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04

So soil conditions

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04

So soil conditions

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04

So soil conditions

βt

(c)


0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04


βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04


βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04


βt

(c)






2s tot] 4ζ2sω

2sσ

2_usr+ ω4





0 01 02 03 04 05 060

02040608

1



ζb = 03 (LDRB)

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06025

03

035

04

ν t op

t=ϖ t

opt

ϖb



ζb = 03 (LDRB)

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t



ζb = 03 (LDRB)

βt

(c)


0 01 02 03 04 05 060

02

04

06

081

σ2uuml s t

otσ

2 uuml s0 to

t

βt



(a)

001

01

10

1

50

0 01 02 03 04 05 06βt

Stro

ke =

σ2 u tσ

2 u b0




ζb = 03

MediumSoWhite-noise

Firm

(b)















ms

csks

kt ctkb cb

mb

mt

bt

uumlg t












EXIT





Yes

No




Seismicretrofitting





with s H

100 016 m


030⟶Δhlt 00096 m





radicsumNminus1

i0

2S(iΔω)Δωradic





H = 32 hc = 06

hc = 06

hc = 06

hc = 05

hc = 04

hb = 06

hb = 06

hb = 07

hb = 07

hb = 07

h b

h c

hc

H = 32

H = 32

H = 32

H = 32

Beamsection

03

0303

kb cbkt ct

bt

L = 45 L = 45 L = 45

Columnsection

L = 45 L = 45




1 + μminus1b




sic2sidsi the














0acc 50

5 10 15 20 25 30ndash04

ndash02

0

02

04u s

5 (m

)

t (s)


(a)

acc 1000 5 10 15 20 25 30

ndash025

ndash015

ndash005

005

015

025

u s5

(m)

t (s)


(b)

acc 500 5 10 15 20 25 30

ndash06

ndash03

0

03

06

u t (m

)

t (s)


(c)

0 5 10 15 20 25 30ndash04

ndash02

0

02

04

u t (m

)

t (s)


acc 100

(d)










TMDstroke



2nd interstorydrift




Baseshear

Vb(kN)

Kineticenergy

Ts(kNm)

Strainenergy

Es(Nm)


858 1727 8231 2290 3819 18798 792 mdash


387 820 4234 1080 988 5025 356 585




506 1048 5217 1380 1573 7726 467 mdash



440 1048 5217 1220 1573 7726 400 mdash






TMDstroke



2nd interstorydrift




Baseshear

Vb (kN)

Kineticenergy

Ts (kNm)

Strainenergy

Es(Nm)



1359 3037 18359 3900 7031 32017 1239 1847




1632 3489 2045 4523 9765 42081 1496 mdash



1465 3489 2045 4160 9765 42081 1329 mdash





0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 50

t (s)

F (k

N)


(a)

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 100

t (s)

F (k

N)


(b)


0 01 02 03 04 05 06 07Basement

012345

Displacement (m)

Stor

y nu

mbe

r


Conventional BIS


(a)


Conventional BIS


0

1

2

3

4

5

Stor

y nu

mbe

r


(b)

0

1

2

3

4

5

0 02 04 06 08 1

Stor

y nu

mbe

r



Conventional BIS


(c)






ktmeffradic




0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro


u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)






0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



minx





2us0




0 01 02 03 04 05 060

02040608

1

βt

μt = 001μt = 01μt = 04


σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

βt

μt = 001μt = 01μt = 04


ν t op

t=ϖ t

opt

ϖb

(b)

0 01 02 03 04 05 060

01

02

03

04

βt

μt = 001μt = 01μt = 04


ζ t op

t

(c)


0 01 02 03 04 05 060

02040608

1

βt

μt = 001μt = 01μt = 04


σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

βt

μt = 001μt = 01μt = 04


ν t op

t=ϖ t

opt

ϖb

(b)

0 01 02 03 04 05 060

01

02

03

04

βt

μt = 001μt = 01μt = 04


opt

(c)







0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04

So soil conditions

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04

So soil conditions

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04

So soil conditions

βt

(c)


0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04


βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04


βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04


βt

(c)






2s tot] 4ζ2sω

2sσ

2_usr+ ω4





0 01 02 03 04 05 060

02040608

1



ζb = 03 (LDRB)

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06025

03

035

04

ν t op

t=ϖ t

opt

ϖb



ζb = 03 (LDRB)

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t



ζb = 03 (LDRB)

βt

(c)


0 01 02 03 04 05 060

02

04

06

081

σ2uuml s t

otσ

2 uuml s0 to

t

βt



(a)

001

01

10

1

50

0 01 02 03 04 05 06βt

Stro

ke =

σ2 u tσ

2 u b0




ζb = 03

MediumSoWhite-noise

Firm

(b)















ms

csks

kt ctkb cb

mb

mt

bt

uumlg t












EXIT





Yes

No




Seismicretrofitting





with s H

100 016 m


030⟶Δhlt 00096 m





radicsumNminus1

i0

2S(iΔω)Δωradic





H = 32 hc = 06

hc = 06

hc = 06

hc = 05

hc = 04

hb = 06

hb = 06

hb = 07

hb = 07

hb = 07

h b

h c

hc

H = 32

H = 32

H = 32

H = 32

Beamsection

03

0303

kb cbkt ct

bt

L = 45 L = 45 L = 45

Columnsection

L = 45 L = 45




1 + μminus1b




sic2sidsi the














0acc 50

5 10 15 20 25 30ndash04

ndash02

0

02

04u s

5 (m

)

t (s)


(a)

acc 1000 5 10 15 20 25 30

ndash025

ndash015

ndash005

005

015

025

u s5

(m)

t (s)


(b)

acc 500 5 10 15 20 25 30

ndash06

ndash03

0

03

06

u t (m

)

t (s)


(c)

0 5 10 15 20 25 30ndash04

ndash02

0

02

04

u t (m

)

t (s)


acc 100

(d)










TMDstroke



2nd interstorydrift




Baseshear

Vb(kN)

Kineticenergy

Ts(kNm)

Strainenergy

Es(Nm)


858 1727 8231 2290 3819 18798 792 mdash


387 820 4234 1080 988 5025 356 585




506 1048 5217 1380 1573 7726 467 mdash



440 1048 5217 1220 1573 7726 400 mdash






TMDstroke



2nd interstorydrift




Baseshear

Vb (kN)

Kineticenergy

Ts (kNm)

Strainenergy

Es(Nm)



1359 3037 18359 3900 7031 32017 1239 1847




1632 3489 2045 4523 9765 42081 1496 mdash



1465 3489 2045 4160 9765 42081 1329 mdash





0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 50

t (s)

F (k

N)


(a)

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 100

t (s)

F (k

N)


(b)


0 01 02 03 04 05 06 07Basement

012345

Displacement (m)

Stor

y nu

mbe

r


Conventional BIS


(a)


Conventional BIS


0

1

2

3

4

5

Stor

y nu

mbe

r


(b)

0

1

2

3

4

5

0 02 04 06 08 1

Stor

y nu

mbe

r



Conventional BIS


(c)






ktmeffradic




0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro


u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)






0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04

So soil conditions

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04

So soil conditions

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04

So soil conditions

βt

(c)


0 01 02 03 04 05 060

02040608

1

μt = 001μt = 01μt = 04


βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06015

02025

03035

04

ν t op

t=ϖ t

opt

ϖb

μt = 001μt = 01μt = 04


βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t

μt = 001μt = 01μt = 04


βt

(c)






2s tot] 4ζ2sω

2sσ

2_usr+ ω4





0 01 02 03 04 05 060

02040608

1



ζb = 03 (LDRB)

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06025

03

035

04

ν t op

t=ϖ t

opt

ϖb



ζb = 03 (LDRB)

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t



ζb = 03 (LDRB)

βt

(c)


0 01 02 03 04 05 060

02

04

06

081

σ2uuml s t

otσ

2 uuml s0 to

t

βt



(a)

001

01

10

1

50

0 01 02 03 04 05 06βt

Stro

ke =

σ2 u tσ

2 u b0




ζb = 03

MediumSoWhite-noise

Firm

(b)















ms

csks

kt ctkb cb

mb

mt

bt

uumlg t












EXIT





Yes

No




Seismicretrofitting





with s H

100 016 m


030⟶Δhlt 00096 m





radicsumNminus1

i0

2S(iΔω)Δωradic





H = 32 hc = 06

hc = 06

hc = 06

hc = 05

hc = 04

hb = 06

hb = 06

hb = 07

hb = 07

hb = 07

h b

h c

hc

H = 32

H = 32

H = 32

H = 32

Beamsection

03

0303

kb cbkt ct

bt

L = 45 L = 45 L = 45

Columnsection

L = 45 L = 45




1 + μminus1b




sic2sidsi the














0acc 50

5 10 15 20 25 30ndash04

ndash02

0

02

04u s

5 (m

)

t (s)


(a)

acc 1000 5 10 15 20 25 30

ndash025

ndash015

ndash005

005

015

025

u s5

(m)

t (s)


(b)

acc 500 5 10 15 20 25 30

ndash06

ndash03

0

03

06

u t (m

)

t (s)


(c)

0 5 10 15 20 25 30ndash04

ndash02

0

02

04

u t (m

)

t (s)


acc 100

(d)










TMDstroke



2nd interstorydrift




Baseshear

Vb(kN)

Kineticenergy

Ts(kNm)

Strainenergy

Es(Nm)


858 1727 8231 2290 3819 18798 792 mdash


387 820 4234 1080 988 5025 356 585




506 1048 5217 1380 1573 7726 467 mdash



440 1048 5217 1220 1573 7726 400 mdash






TMDstroke



2nd interstorydrift




Baseshear

Vb (kN)

Kineticenergy

Ts (kNm)

Strainenergy

Es(Nm)



1359 3037 18359 3900 7031 32017 1239 1847




1632 3489 2045 4523 9765 42081 1496 mdash



1465 3489 2045 4160 9765 42081 1329 mdash





0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 50

t (s)

F (k

N)


(a)

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 100

t (s)

F (k

N)


(b)


0 01 02 03 04 05 06 07Basement

012345

Displacement (m)

Stor

y nu

mbe

r


Conventional BIS


(a)


Conventional BIS


0

1

2

3

4

5

Stor

y nu

mbe

r


(b)

0

1

2

3

4

5

0 02 04 06 08 1

Stor

y nu

mbe

r



Conventional BIS


(c)






ktmeffradic




0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro


u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)






0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





2s tot] 4ζ2sω

2sσ

2_usr+ ω4





0 01 02 03 04 05 060

02040608

1



ζb = 03 (LDRB)

βt

σ2 u sm

inσ

2 u s0

(a)

0 01 02 03 04 05 06025

03

035

04

ν t op

t=ϖ t

opt

ϖb



ζb = 03 (LDRB)

βt

(b)

0 01 02 03 04 05 060

01

02

03

04

ζ t op

t



ζb = 03 (LDRB)

βt

(c)


0 01 02 03 04 05 060

02

04

06

081

σ2uuml s t

otσ

2 uuml s0 to

t

βt



(a)

001

01

10

1

50

0 01 02 03 04 05 06βt

Stro

ke =

σ2 u tσ

2 u b0




ζb = 03

MediumSoWhite-noise

Firm

(b)















ms

csks

kt ctkb cb

mb

mt

bt

uumlg t












EXIT





Yes

No




Seismicretrofitting





with s H

100 016 m


030⟶Δhlt 00096 m





radicsumNminus1

i0

2S(iΔω)Δωradic





H = 32 hc = 06

hc = 06

hc = 06

hc = 05

hc = 04

hb = 06

hb = 06

hb = 07

hb = 07

hb = 07

h b

h c

hc

H = 32

H = 32

H = 32

H = 32

Beamsection

03

0303

kb cbkt ct

bt

L = 45 L = 45 L = 45

Columnsection

L = 45 L = 45




1 + μminus1b




sic2sidsi the














0acc 50

5 10 15 20 25 30ndash04

ndash02

0

02

04u s

5 (m

)

t (s)


(a)

acc 1000 5 10 15 20 25 30

ndash025

ndash015

ndash005

005

015

025

u s5

(m)

t (s)


(b)

acc 500 5 10 15 20 25 30

ndash06

ndash03

0

03

06

u t (m

)

t (s)


(c)

0 5 10 15 20 25 30ndash04

ndash02

0

02

04

u t (m

)

t (s)


acc 100

(d)










TMDstroke



2nd interstorydrift




Baseshear

Vb(kN)

Kineticenergy

Ts(kNm)

Strainenergy

Es(Nm)


858 1727 8231 2290 3819 18798 792 mdash


387 820 4234 1080 988 5025 356 585




506 1048 5217 1380 1573 7726 467 mdash



440 1048 5217 1220 1573 7726 400 mdash






TMDstroke



2nd interstorydrift




Baseshear

Vb (kN)

Kineticenergy

Ts (kNm)

Strainenergy

Es(Nm)



1359 3037 18359 3900 7031 32017 1239 1847




1632 3489 2045 4523 9765 42081 1496 mdash



1465 3489 2045 4160 9765 42081 1329 mdash





0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 50

t (s)

F (k

N)


(a)

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 100

t (s)

F (k

N)


(b)


0 01 02 03 04 05 06 07Basement

012345

Displacement (m)

Stor

y nu

mbe

r


Conventional BIS


(a)


Conventional BIS


0

1

2

3

4

5

Stor

y nu

mbe

r


(b)

0

1

2

3

4

5

0 02 04 06 08 1

Stor

y nu

mbe

r



Conventional BIS


(c)






ktmeffradic




0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro


u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)






0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia














ms

csks

kt ctkb cb

mb

mt

bt

uumlg t












EXIT





Yes

No




Seismicretrofitting





with s H

100 016 m


030⟶Δhlt 00096 m





radicsumNminus1

i0

2S(iΔω)Δωradic





H = 32 hc = 06

hc = 06

hc = 06

hc = 05

hc = 04

hb = 06

hb = 06

hb = 07

hb = 07

hb = 07

h b

h c

hc

H = 32

H = 32

H = 32

H = 32

Beamsection

03

0303

kb cbkt ct

bt

L = 45 L = 45 L = 45

Columnsection

L = 45 L = 45




1 + μminus1b




sic2sidsi the














0acc 50

5 10 15 20 25 30ndash04

ndash02

0

02

04u s

5 (m

)

t (s)


(a)

acc 1000 5 10 15 20 25 30

ndash025

ndash015

ndash005

005

015

025

u s5

(m)

t (s)


(b)

acc 500 5 10 15 20 25 30

ndash06

ndash03

0

03

06

u t (m

)

t (s)


(c)

0 5 10 15 20 25 30ndash04

ndash02

0

02

04

u t (m

)

t (s)


acc 100

(d)










TMDstroke



2nd interstorydrift




Baseshear

Vb(kN)

Kineticenergy

Ts(kNm)

Strainenergy

Es(Nm)


858 1727 8231 2290 3819 18798 792 mdash


387 820 4234 1080 988 5025 356 585




506 1048 5217 1380 1573 7726 467 mdash



440 1048 5217 1220 1573 7726 400 mdash






TMDstroke



2nd interstorydrift




Baseshear

Vb (kN)

Kineticenergy

Ts (kNm)

Strainenergy

Es(Nm)



1359 3037 18359 3900 7031 32017 1239 1847




1632 3489 2045 4523 9765 42081 1496 mdash



1465 3489 2045 4160 9765 42081 1329 mdash





0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 50

t (s)

F (k

N)


(a)

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 100

t (s)

F (k

N)


(b)


0 01 02 03 04 05 06 07Basement

012345

Displacement (m)

Stor

y nu

mbe

r


Conventional BIS


(a)


Conventional BIS


0

1

2

3

4

5

Stor

y nu

mbe

r


(b)

0

1

2

3

4

5

0 02 04 06 08 1

Stor

y nu

mbe

r



Conventional BIS


(c)






ktmeffradic




0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro


u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)






0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











EXIT





Yes

No




Seismicretrofitting





with s H

100 016 m


030⟶Δhlt 00096 m





radicsumNminus1

i0

2S(iΔω)Δωradic





H = 32 hc = 06

hc = 06

hc = 06

hc = 05

hc = 04

hb = 06

hb = 06

hb = 07

hb = 07

hb = 07

h b

h c

hc

H = 32

H = 32

H = 32

H = 32

Beamsection

03

0303

kb cbkt ct

bt

L = 45 L = 45 L = 45

Columnsection

L = 45 L = 45




1 + μminus1b




sic2sidsi the














0acc 50

5 10 15 20 25 30ndash04

ndash02

0

02

04u s

5 (m

)

t (s)


(a)

acc 1000 5 10 15 20 25 30

ndash025

ndash015

ndash005

005

015

025

u s5

(m)

t (s)


(b)

acc 500 5 10 15 20 25 30

ndash06

ndash03

0

03

06

u t (m

)

t (s)


(c)

0 5 10 15 20 25 30ndash04

ndash02

0

02

04

u t (m

)

t (s)


acc 100

(d)










TMDstroke



2nd interstorydrift




Baseshear

Vb(kN)

Kineticenergy

Ts(kNm)

Strainenergy

Es(Nm)


858 1727 8231 2290 3819 18798 792 mdash


387 820 4234 1080 988 5025 356 585




506 1048 5217 1380 1573 7726 467 mdash



440 1048 5217 1220 1573 7726 400 mdash






TMDstroke



2nd interstorydrift




Baseshear

Vb (kN)

Kineticenergy

Ts (kNm)

Strainenergy

Es(Nm)



1359 3037 18359 3900 7031 32017 1239 1847




1632 3489 2045 4523 9765 42081 1496 mdash



1465 3489 2045 4160 9765 42081 1329 mdash





0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 50

t (s)

F (k

N)


(a)

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 100

t (s)

F (k

N)


(b)


0 01 02 03 04 05 06 07Basement

012345

Displacement (m)

Stor

y nu

mbe

r


Conventional BIS


(a)


Conventional BIS


0

1

2

3

4

5

Stor

y nu

mbe

r


(b)

0

1

2

3

4

5

0 02 04 06 08 1

Stor

y nu

mbe

r



Conventional BIS


(c)






ktmeffradic




0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro


u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)






0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




with s H

100 016 m


030⟶Δhlt 00096 m





radicsumNminus1

i0

2S(iΔω)Δωradic





H = 32 hc = 06

hc = 06

hc = 06

hc = 05

hc = 04

hb = 06

hb = 06

hb = 07

hb = 07

hb = 07

h b

h c

hc

H = 32

H = 32

H = 32

H = 32

Beamsection

03

0303

kb cbkt ct

bt

L = 45 L = 45 L = 45

Columnsection

L = 45 L = 45




1 + μminus1b




sic2sidsi the














0acc 50

5 10 15 20 25 30ndash04

ndash02

0

02

04u s

5 (m

)

t (s)


(a)

acc 1000 5 10 15 20 25 30

ndash025

ndash015

ndash005

005

015

025

u s5

(m)

t (s)


(b)

acc 500 5 10 15 20 25 30

ndash06

ndash03

0

03

06

u t (m

)

t (s)


(c)

0 5 10 15 20 25 30ndash04

ndash02

0

02

04

u t (m

)

t (s)


acc 100

(d)










TMDstroke



2nd interstorydrift




Baseshear

Vb(kN)

Kineticenergy

Ts(kNm)

Strainenergy

Es(Nm)


858 1727 8231 2290 3819 18798 792 mdash


387 820 4234 1080 988 5025 356 585




506 1048 5217 1380 1573 7726 467 mdash



440 1048 5217 1220 1573 7726 400 mdash






TMDstroke



2nd interstorydrift




Baseshear

Vb (kN)

Kineticenergy

Ts (kNm)

Strainenergy

Es(Nm)



1359 3037 18359 3900 7031 32017 1239 1847




1632 3489 2045 4523 9765 42081 1496 mdash



1465 3489 2045 4160 9765 42081 1329 mdash





0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 50

t (s)

F (k

N)


(a)

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 100

t (s)

F (k

N)


(b)


0 01 02 03 04 05 06 07Basement

012345

Displacement (m)

Stor

y nu

mbe

r


Conventional BIS


(a)


Conventional BIS


0

1

2

3

4

5

Stor

y nu

mbe

r


(b)

0

1

2

3

4

5

0 02 04 06 08 1

Stor

y nu

mbe

r



Conventional BIS


(c)






ktmeffradic




0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro


u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)






0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



1 + μminus1b




sic2sidsi the














0acc 50

5 10 15 20 25 30ndash04

ndash02

0

02

04u s

5 (m

)

t (s)


(a)

acc 1000 5 10 15 20 25 30

ndash025

ndash015

ndash005

005

015

025

u s5

(m)

t (s)


(b)

acc 500 5 10 15 20 25 30

ndash06

ndash03

0

03

06

u t (m

)

t (s)


(c)

0 5 10 15 20 25 30ndash04

ndash02

0

02

04

u t (m

)

t (s)


acc 100

(d)










TMDstroke



2nd interstorydrift




Baseshear

Vb(kN)

Kineticenergy

Ts(kNm)

Strainenergy

Es(Nm)


858 1727 8231 2290 3819 18798 792 mdash


387 820 4234 1080 988 5025 356 585




506 1048 5217 1380 1573 7726 467 mdash



440 1048 5217 1220 1573 7726 400 mdash






TMDstroke



2nd interstorydrift




Baseshear

Vb (kN)

Kineticenergy

Ts (kNm)

Strainenergy

Es(Nm)



1359 3037 18359 3900 7031 32017 1239 1847




1632 3489 2045 4523 9765 42081 1496 mdash



1465 3489 2045 4160 9765 42081 1329 mdash





0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 50

t (s)

F (k

N)


(a)

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 100

t (s)

F (k

N)


(b)


0 01 02 03 04 05 06 07Basement

012345

Displacement (m)

Stor

y nu

mbe

r


Conventional BIS


(a)


Conventional BIS


0

1

2

3

4

5

Stor

y nu

mbe

r


(b)

0

1

2

3

4

5

0 02 04 06 08 1

Stor

y nu

mbe

r



Conventional BIS


(c)






ktmeffradic




0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro


u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)






0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






0acc 50

5 10 15 20 25 30ndash04

ndash02

0

02

04u s

5 (m

)

t (s)


(a)

acc 1000 5 10 15 20 25 30

ndash025

ndash015

ndash005

005

015

025

u s5

(m)

t (s)


(b)

acc 500 5 10 15 20 25 30

ndash06

ndash03

0

03

06

u t (m

)

t (s)


(c)

0 5 10 15 20 25 30ndash04

ndash02

0

02

04

u t (m

)

t (s)


acc 100

(d)










TMDstroke



2nd interstorydrift




Baseshear

Vb(kN)

Kineticenergy

Ts(kNm)

Strainenergy

Es(Nm)


858 1727 8231 2290 3819 18798 792 mdash


387 820 4234 1080 988 5025 356 585




506 1048 5217 1380 1573 7726 467 mdash



440 1048 5217 1220 1573 7726 400 mdash






TMDstroke



2nd interstorydrift




Baseshear

Vb (kN)

Kineticenergy

Ts (kNm)

Strainenergy

Es(Nm)



1359 3037 18359 3900 7031 32017 1239 1847




1632 3489 2045 4523 9765 42081 1496 mdash



1465 3489 2045 4160 9765 42081 1329 mdash





0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 50

t (s)

F (k

N)


(a)

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 100

t (s)

F (k

N)


(b)


0 01 02 03 04 05 06 07Basement

012345

Displacement (m)

Stor

y nu

mbe

r


Conventional BIS


(a)


Conventional BIS


0

1

2

3

4

5

Stor

y nu

mbe

r


(b)

0

1

2

3

4

5

0 02 04 06 08 1

Stor

y nu

mbe

r



Conventional BIS


(c)






ktmeffradic




0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro


u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)






0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









TMDstroke



2nd interstorydrift




Baseshear

Vb(kN)

Kineticenergy

Ts(kNm)

Strainenergy

Es(Nm)


858 1727 8231 2290 3819 18798 792 mdash


387 820 4234 1080 988 5025 356 585




506 1048 5217 1380 1573 7726 467 mdash



440 1048 5217 1220 1573 7726 400 mdash






TMDstroke



2nd interstorydrift




Baseshear

Vb (kN)

Kineticenergy

Ts (kNm)

Strainenergy

Es(Nm)



1359 3037 18359 3900 7031 32017 1239 1847




1632 3489 2045 4523 9765 42081 1496 mdash



1465 3489 2045 4160 9765 42081 1329 mdash





0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 50

t (s)

F (k

N)


(a)

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 100

t (s)

F (k

N)


(b)


0 01 02 03 04 05 06 07Basement

012345

Displacement (m)

Stor

y nu

mbe

r


Conventional BIS


(a)


Conventional BIS


0

1

2

3

4

5

Stor

y nu

mbe

r


(b)

0

1

2

3

4

5

0 02 04 06 08 1

Stor

y nu

mbe

r



Conventional BIS


(c)






ktmeffradic




0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro


u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)






0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 50

t (s)

F (k

N)


(a)

0 5 10 15 20 25 30ndash200

ndash100

0

100

200

acc 100

t (s)

F (k

N)


(b)


0 01 02 03 04 05 06 07Basement

012345

Displacement (m)

Stor

y nu

mbe

r


Conventional BIS


(a)


Conventional BIS


0

1

2

3

4

5

Stor

y nu

mbe

r


(b)

0

1

2

3

4

5

0 02 04 06 08 1

Stor

y nu

mbe

r



Conventional BIS


(c)






ktmeffradic




0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro


u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)






0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





ktmeffradic




0 10 20 30 40 50ndash02

ndash01

0

01

02

El centro


u s5 (

m)

t (s)

(a)

0 10 20 30 40ndash02

ndash01

0

01

02

Loma prieta


u s5 (

m)

t (s)

(b)






0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





0 01 02 03Basement

0

1

2

3

4

5El centro

Stor

y nu

mbe

r

Displacement (m)

(a)



0

1

2

3

4

5

Stor

y nu

mbe

r

(b)


0 02 04 06 08 10

1

2

3

4

5

Stor

y nu

mbe

r


(c)

0 01 02 03Basement

0

1

2

3

4

5Loma prieta

Displacement (m)

Stor

y nu

mbe

r


(d)

0 02 04 060

1

2

3

4

5



Stor

y nu

mbe

r

(e)

0 02 04 06 08 10

1

2

3

4

5



Stor

y nu

mbe

r

(f)












1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











1

125

15

175

2

225

05 075 125 15 175 21ωtωt opt[ndash]


ζt = ζt opt yy o

pt[ndash

]

(a)

05 075 15 175 21

11

12

13

14

1 125

ωt = ωt opt


ζtζt opt[ndash]

yy o

pt[ndash

]

(b)







12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






12

125

15

215

175

15

2

1 105 05 ωtωt opt

u s5

u s5

opt [ndash]

ζtζt opt

(a)

12

125

215

15

15

175

1 105 05 ωtωt opt

ζtζt opt

V bV

b op

t [ndash]

(b)

1 1

1 1

12

1 2

13

1 3

1 4

1 4

1 5

1 5

1 6

1 7

1 8

05 1 15 205

1

15

2

ωtωt opt[ndash]

ζ tζ t

opt [ndash]

(c)

1 1

11

1 2

121 3

1 3

14

1 4

151 6


ζ tζ t

opt [ndash]

1

05

15

2

(d)







Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






Acknowledgments


References






















































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia
























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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