Structural Dynamics & Vibration Control Lab., KAIST 1 Structural Vibration Control Using Semiactive Tuned Mass Damper Han-Rok Ji, Graduate Student, KAIST,

Structural Dynamics & Vibration Control Lab., KAISTStructural Dynamics & Vibration Control Lab., KAIST 1 1

Structural Vibration Control

Using Semiactive Tuned Mass Damper

Structural Vibration Control

Using Semiactive Tuned Mass Damper

Han-Rok Ji, Graduate Student, KAIST, Korea

Yeong-Jong Moon, Ph. D. Candidate, KAIST, Korea

Chun-Ho Kim, Professor, Joongbu University, Korea

In-Won Lee, Professor, KAIST, Korea

Han-Rok Ji, Graduate Student, KAIST, Korea

Yeong-Jong Moon, Ph. D. Candidate, KAIST, Korea

Chun-Ho Kim, Professor, Joongbu University, Korea

In-Won Lee, Professor, KAIST, Korea

The Eighteenth KKCNN Symposium on Civil EngineeringThe Eighteenth KKCNN Symposium on Civil Engineering


Introduction

Semiactive Tuned Mass Damper

Numerical Analysis

Conclusions

CONTENTS


Introduction

Tuned Mass Damper

― widely used mechanical damping device

― Simple and efficient vibration control system

― No external power, energy dissipation, inherent reliability

― Restricted performance resulted from the fixed parameters


― Alternative device of conventional TMD ― Improved control performance with stability of TMD― High robustness and adaptability


Objective

Analytical study on semiactive TMD using MR damper

for mitigating the vibration of structures

Application of various semiactive control algorithms to MR damper

Robustness analysis for the semiactive TMD system



m1

k1

c1

m2

c(t)

x1

x2

k2

m1

gxm

m

x

x

kk

kkk

x

x

cc

ccc

x

x

m

m

1

1

0

0

0

0

2

1

2

1

22

221

2

1

22

221

2

1

2

1

― Equation of Motion― Equation of Motion

(1) (1)

SDOF system with semiactive TMDSDOF system with semiactive TMD

– Controllable damping device is

installed in the place of passive dashpot.

– Produce the additional control effect

to the primary structure.

– Controllable damping device is

installed in the place of passive dashpot.

– Produce the additional control effect

to the primary structure.


)Vu(u

ucc)u(cc

ucc)u(cc

u)u(

)yx(kxczcc

y

)yx(Az)yx(zzyxz

)xx(kycf

ba

ba

ba

nn

0000

1111

0010

1

011

1

c0 c1 k1

k0

c1 c0 k0

k1

Modified Bouc-Wen Model

Bouc-Wen

― modified Bouc-Wen model (Spencer et al., 1997)

(2) (2)

• Dynamic model of MR damper


Semiactive Control Algorithms

― on-off velocity based groundhook control

― on-off displacement based groundhook control

― clipped optimal algorithm

― maximum energy dissipation algorithm


maxVVthen,vvvif 0211

• On-off velocity based groundhook control (Koo et al. 2003)

― Based on velocity of primary system (v1 ) and TMD (v2 )

minVVthen,vvvif 0211

(3) (3)

• On-off displacement based groundhook control (Koo et al. 2003)

(4) (4)

― Based on velocity of primary system (v1 ) and TMD (v2 )

displacement of primary system (x1 )

maxVVthen,vvxif 0211

minVVthen,vvxif 0211


― linear optimal controller and clipped algorithm

Fc : desired damper force by optimal controller

Fd : measured damper force

ddcmax FFFHVV

• Clipped optimal algorithm (Dyke et al, 1996)

(5) (5)

)Fx(HVV dmax

• Maximum energy dissipation algorithm (Jansen and Dyke, 2000)

(6) (6)

― Control voltage is determined so that the structure dissipates the maximum energy

Fd : measured damper force


kg

,

,

,

M

500100

050010

005001

m

N

..

...

..

K 610

12120

122412

01224

m

secN

...

...

...

C

9104258410

2587152843

4108431163

gx

• Three-story shear building MR damper

mTMD = 150 kg , kTMD = 36,401 N/m

• Input earthquake excitations

― amplitude scaled El Centro, Hachinohe earthquakes― amplitude scaled El Centro, Hachinohe earthquakes

Numerical Analysis


Value Value

coa 21.0 Nsec/cm a 140 N/cm

cob 3.50 Nsec/cmV b 695 N/cmV

ko 46.9 N/cm 363 cm-2

c1a 283 Nsec/cm 363 cm-2

c1b 2.95 Nsec/cmV A 301

k1 5.00 N/cm n 2

xo 14.3 cm 190 sec-1

• Parameters of MR damper (Spencer et al., 1997)

c0 c1 k1

k0

c1 c0 k0

k1

Modified Bouc-Wen model

Bouc-Wen

― maximum damper force : 1,500 N

― minimum voltage : 0 V

― maximum voltage : 2.25 V


Response of building model

TMDpassive

offpassive

onon-off

DBG

on-off

VBG

clipped

optimalMEDA

Scaled

El Centro

(PGA 0.10g)

J1 0.38 0.39 0.50 0.35 0.39 0.36 0.39

J2 0.37 0.37 0.52 0.33 0.34 0.32 0.34

J3 0.45 0.47 0.50 0.44 0.44 0.43 0.44

Scaled

Hachinohe

(PGA 0.08g)

J1 0.35 0.36 0.51 0.35 0.40 0.36 0.40

J2 0.35 0.35 0.49 0.32 0.39 0.34 0.39

J3 0.38 0.41 0.47 0.36 0.37 0.35 0.37

J1 : normalized peak floor displacement

J2 : normalized peak interstory drift

J3 : normalized peak acceleration


0.2

0.3

0.4

0.5

0.6

TMD passiveoff

passiveon

on-offDBG

on-offVBG

clippedoptimal

MEDA

J₁J₂J₃

0.3

0.35

0.4

0.45

0.5

0.55

TMD passiveoff

passive on on-offDBG

on-offVBG

clippedoptimal

MEDA

J₁J₂J₃

― El Centro earthquake ― Hachinohe earthquake

― The efficiency of semiactive TMD is slightly better than that of TMD.

― Passive on mode has the worst performance.

Nor

mal

ized

val

ue

Nor

mal

ized

val

ue

― Evaluation criteria under two earthquakes


Robustness Analysis

• Response with stiffness matrix perturbation

1KK̂

: amount of perturbation

(-15%, -10%, -5%, +5%, +10% and +15%)

― Perturbed stiffness matrix

(7) (7)

― Real structures can have structural uncertainties in many reasons.

― Control performance of TMD is restricted considerably due to

off-tuning effect.— Stiffness perturbation is considered to verify the robustness of the semiactive TMD


-0.6

-0.3

0

0.3

0.6

0 5 10 15 20

TMD

on-off DBG

-3

-1.5

0

1.5

3

0 5 10 15 20

TMD

on-off DBG

Time (sec)

Inte

rsto

ry d

rift

(cm

)A

ccel

erat

ion

(m

/sec

2 )

Time history with +15% stiffness perturbation under Hachinohe earthquake

― The maximum and RMS values with semiactive TMD are reduced

compared with that of conventional TMD.


0.2

0.4

0.6

0.8

1

1.2

-15% -10% -5% 0% 5% 10% 15%

TMDon-off DBGon-off VBGclipped optiamalMEDA

Nor

mal

ized

pea

k dr

ift

(J 2)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-15% -10% -5% 0% 5% 10% 15%


Nor

mal

ized

pea

k ac

cele

rati

on (

J 3)― Overall performance of semiactive TMD is better than that of TMD.

― Efficient algorithm : on-off DBG control for interstory drift

clipped optimal control for acceleration

― Evaluation criteria under El Centro earthquake


Nor

mal

ized

pea

k dr

ift

(J 2)

Nor

mal

ized

pea

k ac

cele

rati

on (

J 3)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-15% -10% -5% 0% 5% 10% 15%


0.2

0.3

0.4

0.5

0.6

0.7

0.8

-15% -10% -5% 0% 5% 10% 15%

TMD

on-off DBG

on-off VBG

clipped optiamal

MEDA

― Semiactive TMD is superior to conventional TMD.

― On-off DBG and clipped optimal algorithm have sufficient robustness.

― Evaluation criteria under Hachinohe earthquake


― Various semiactive control algorithms are adopted and

the performance of each algorithm is evaluated.

― Various semiactive control algorithms are adopted and

the performance of each algorithm is evaluated.

― Semiactive TMD system shows slightly better performance

than conventional TMD system.

― Semiactive TMD system shows slightly better performance

than conventional TMD system.

― Analytical study on semiactive TMD with MR damper is

performed.

― Analytical study on semiactive TMD with MR damper is

performed.

Conclusions


― Sufficient robustness is obtained under the structural

perturbation with semiactive TMD.

― Sufficient robustness is obtained under the structural

perturbation with semiactive TMD.

― The on-off displacement based groundhook theory and

clipped optimal algorithm is appropriate algorithm for

semiactive TMD system.

― The on-off displacement based groundhook theory and

clipped optimal algorithm is appropriate algorithm for

semiactive TMD system.

Documents

Structural Dynamics & Vibration Control Lab., KAIST 1 Structural Vibration Control Using Semiactive Tuned Mass Damper Han-Rok Ji, Graduate Student, KAIST,