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International Journal of Advanced Engineering Technology E-ISSN 0976-3945
IJAET/Vol.II/ Issue III/July-September, 2011/246-256
Research Article
SEISMIC RESPONSE CONTROL OF A BUILDING
INSTALLED WITH PASSIVE DAMPERS Nitendra G Mahajan*1
and D B Raijiwala2
Address for Correspondence 1Research Scholar, Department of Structural Engineering, Sardar Vallabhbhai National
Institute of Technology, Surat 2Professor, Department of Structural Engineering, Sardar Vallabhbhai National
Institute of Technology, Surat
ABSTRACT: Seismic response control using passive dampers is most cost effective, satisfied the architectural requirement of opening and recent technique to control the vibrations of structures arising due to dynamic loading. This study investigates the influence of mechanical control on structural systems through strategically applying reliable dampers that can modulate the response of building. SAP2000 nonlinear time history analysis program was applied to investigate the effects on building such as normalized base shear, tip displacement, normalized acceleration and energy dissipation of damper element by varying different important parameters namely Earthquake time histories, location of dampers, damping coefficient, damper stiffness, no of story of building. Comparison study is also presented between building installed with dampers, building installed with diagonal bracing, combination of both and simple building to show importance of damping system for reduction of seismic quantities. Finally, the building installed with damping system is very effective and reliable solution to reduce very vital seismic quantities such as base shear, floor displacement, and floor acceleration and also mitigate architectural requirement which cannot be satisfied by shear walls.
KEYWORDS: structural control system, seismic response, Passive dampers, Non linear Time History, SAP2000.
1. INTRODUCTION 1.1 Need and Objectives of the Structural
Control The main objective of Structural engineering field
is to design and construct the safe and stable
structures. The massive earthquake that hit Japan
on March 11 and the tsunami it unleashed have
killed up to 28,000 people and crippled a nuclear
power plant near the northeastern town of
Fukushima that has leaked radiation virtually ever
since. Total damages have been estimated at $300
billion, making it the world's costliest natural
disaster. The disasters have also hurt the Japanese
economy, the world's third largest. Recent Japan
Earthquake of March 2011 has seriously
threatened the safety and property of the residents.
Various types of structural control technologies
have been developed to solve the safety and
functional problems for structures under the
excitation of external force. With current design
procedures, the structures are expected to suffer
significant damage but no collapse if the
earthquake scenario that was considered for its
design occurs. Although this philosophy has been
the standard for many decades, new design
procedures and novel devices are changing the
traditional approach. An example of the new
procedures is the one known as performance-
based design. This methodology will provide the
structural engineer with the tools to predetermine
the amount of damage that the user is willing to
tolerate and design the structure accordingly. On
the other hand, a number of modern mechanical
systems have been proposed in the last two
decades to reduce the structural response (and thus
the amount of damage). Figure 1.1 shows the
Annual earthquake death rate per million
populations in red; smoothed rates in grey. They
are known collectively as “protective devices” and
they include added viscoelastic dampers, viscous
fluid dampers, frictional dampers, hysteretic
dampers, tuned-mass dampers, and base isolation
systems. The devices themselves and their design
methodology are referred to as “passive control
systems”.
Figure 1.1 Annual earthquake death rate per
million.
1.2 Fundamental of Passive Structural Control 1.2.1 Passive Control Systems
Figure 1.1 shows the Conventional System. The
principal function of a passive energy dissipation
system is to reduce the inelastic energy dissipation
demand on the framing system of a structure. The
result is reduced damage to the framing system. A
passive control system (Figure 1.2) may be defined
International Journal of Advanced Engineering Technology E-ISSN 0976-3945
IJAET/Vol.II/ Issue III/July-September, 2011/
as a system which does not require an external
power source for operation and utilizes the motion
of the structure to develop the control forces.
Control forces are developed as a function of
the response of the structure at the location of
the passive control system. The control system and
the structure do not behave as independent
dynamic systems but rather interact with each
other.
Figure 1.1 Conventional System.
Figure 1.2 Passive Control System.
1.2.2 Advantages of passive control system.
• It is usually relatively inexpensive.
• It consumes no external energy.
• It is inherently stable.
• It works even during a major earthquake.
1.2.3 Disadvantages of passive control systems.
The idea of passive control is to dissipate the
vibratory energy in the structural system.
However, this kind of control system provides no
extra assistance, so it cannot adapt to varying
loading conditions. Consequently its effect is
limited. The effectiveness (amount of control) of
passive devices is always limited due to the
passive nature of devices and the random nature of
earthquake events. The passive control does not
make any real time changes in the system.
1.3 Damping System.
The objective of utilizing dampers is to reduce
structure responses and to mitigate damage or
collapse of structures from severe earthquakes by
participating energy dissipations. As a successful
application, installation of dampers in an existing
building structure, which does not possess
sufficient lateral stiffness, enables control of the
story drift within the required limitation and
maintains its desired functions during an
earthquake event. Since the first application of
dampers in structural engineering took place in
1960s, abundant research work has been
conducted to study the mechanisms of dampers
and the behavior of damped structures. With the
invention of different types of damping devices,
improvement of modeling techniques and
development of new computational
methodologies, use of dampers has become a
mature technology in designing of new structures
and retrofitting of existing facilities.
1.3.1 Definitions:
1.3.1.1 Damping device:
A flexible structural element of the damping
system that dissipates energy due to relative
motion of each end of the device. Damping
devices include all pins, bolts, gusset plates, brace
extensions, and other components required to
connect damping devices to the other elements of
the structure. Damping devices may be classified
as either displacement dependent or velocity-
dependent, or a combination thereof, and may be
configured to act in either a linear or nonlinear
manner.
1.3.1.2 Damping System:
The collection of structural elements that includes
all the individual damping devices, all structural
elements or bracing required to transfer forces
from damping devices to the base of the structure,
and the structural elements required to transfer
forces from damping devices to the seismic force-
resisting system.
1.3.1.3 Displacement-dependent Damping
device:
The force response of a displacement-dependent
damping device is primarily a function of the
relative displacement, between each end of the
device. The response is substantially independent
of the relative velocity between each end of the
devices, and/or the excitation frequency.
1.3.1.4 Velocity- dependent Damping device:
The force-displacement relation for a velocity-
dependent damping device is primarily a function
of the relative velocity between each end of the
device, and could also be a function of the relative
displacement between each end of the device.
2. GOVERNING EQUATIONS AND
MATHEMATICAL MODEL OF MOTION 2.1Single-Degree-of-Freedom Motion Equations
A damping system is usually defined as a
collection of dampers, connections between
dampers and structural members, and structural
members transferring forces between damping
devices and the seismic force-resisting system or
the foundation. Figure 2.1 illustrates both
systems in a structural frame elevation. On the
basis of the location of the damping system, the
damping device can be classified as internal or
external.
International Journal of Advanced Engineering Technology E-ISSN 0976-3945
IJAET/Vol.II/ Issue III/July-September, 2011/246-256
Figure 2.1 damping device and damping system.
Development of single-degree-of-freedom (SDOF)
motion equations can be depicted from a single-story
building structure installed with a damping system,
which is schematically shown in Figure 2.2. The
mass of this structure, assuming it is simply lumped
at the roof level, is denoted as m. To consider the
nonlinear behavior of the building structure, a
general expression is utilized to define the structural
force, Q, instead of ksx, where ks is linear lateral
stiffness of the structure and x, simplified from x(t),
represents roof displacement or deflection of the
structure at any time t. The structural damping
coefficient is designated as cs. Force, P, is defined
along the movement of the damping device.
Accordingly, its horizontal component becomes D =
P cos φ , where angle, φ , relies on assembly
configurations of damping device and bracings. For
the damping devices connected by diagonal bracings
to the building structure, the angle, φ , represents the
damping device’s inclination to the horizontal
movement of the structure.
For common configurations of damping devices
assembled with diagonal or chevron bracings, the
axial stiffness of bracings is usually much stronger
than that of the damping device and the movement
or deformation of the damping system is
dominantly contributed by the damping device.
Accordingly, the bracings can be reasonably
assumed to be rigid components with infinite
stiffness.
Figure 2.2 Mathematical Model SDOF structures with damping devices.
International Journal of Advanced Engineering Technology E-ISSN 0976-3945
IJAET/Vol.II/ Issue III/July-September, 2011/246-256
On the basis of the assumption of infinite stiffness
of the bracings and the well-known equilibrium
condition, SDOF motion equation of the damped
structure is easily expressed as follows:
gs xmQDxcxm &&&&& −=+++
or
gs xmQPxcxm &&&&& −=+++ φcos …2.1
Where the structural acceleration, x&& , and the
ground acceleration, x&& g, are designated from
simplified notations of x&& (t) and x&& g(t),
respectively. On the basis of damper mechanical
properties, damping devices can be classified as
two major categories: (1) velocity dependent and
(2) displacement dependent. Velocity-dependent
damping devices include fluid viscous damper,
fluid viscoelastic damper, and solid viscoelastic
damper, whereas displacement dependent
damping devices consist of friction damper and
metallic yielding damper. Figure 2.3 represents
typical relations between the damping force and
its displacement of linear or nonlinear viscous
dampers, and solid or fluid viscoelastic dampers.
Supported by test results for linear fluid viscous
damper, the damping force, P, can be simply
depicted as a linear relation to its velocity:
lcp d&= ……2.2
Where cd is the damping coefficient of the fluid
viscous damper, while l& represents the relative
velocity of the damper in the direction of P. As
shown in Figure 3.2, l and x remain the
following relation.
φcosxl = and φcosxl && = ……2.3
Thus,
φcosxcP d&= , or φ2cosxcD d
&= …… 2.4
If the fluid viscous damper exhibits nonlinear
behavior to its relative velocity, then the force of a
nonlinear fluid viscous damper, P, has the
following relation to its movement
αα
φcos)sin( xcllcP dd&&& == or )sin(cos 1 xxcD d
&& φαα +=
……2.5
Where α is the velocity exponent. According to
mechanical properties of a solid viscoelastic
damper, the damper force features a function of
its relative velocity to displacement, which can
be simplified in terms of effective damping
coefficient, cd, and effective stiffness, kd:
φφ coscos xkxclklcP dddd +=+= && or φφ 22 coscos xkxcP dd += &
……2.6
Multiple-Degree-of-Freedom Motion Equations
A sketch of a multistory structure installed with
damping system is shown in Figure 2.3. Applying
the equilibrium conditions at the roof level n, and
using relative displacement, xn, the motion
equation due to the ground acceleration, , is
derived as
gnnnnnnsnn xmQDxxcxm &&&&&& −=++−+ − )( 1,.. 2.7
gnnnnnnnsnn xmQPxxcxm &&&&&& −=++−+ − φcos)( 1, ..2.8
where mn is the roof mass and cs,n is denoted as
the structural damping between the roof and the
story below the roof. xn , and xn−1 are utilized to
identify the relative displacement at the roof and
the story below. For the structural force between
the roof level and the story below, a general
expression of Qn , is also, used to represent elastic
or inelastic behavior of the seismic force-resisting
system. According to material properties of the
structure, Qn can be idealized as a linear model,
elastoplastic model, bilinear model, or other types
of models. In Equations 2.7 and 2.8, Pn and Dn are
used to define the axial force and its horizontal
component of damping devices between the roof
and the story below. The specific expression of
the damping force and its relative velocity or
relative displacement needs to be determined by
selected damping devices. φ n presents the angle
between the axial force and the horizontal
component of the damping device.
By applying the same methodology used for
Equation 3.5, the motion equation at story m is
identified as below:
.2.9..........…
)()(
11
11,1,
gnmmmm
mmmsmmmsmm
xmQQDD
xxcxxcxm
&&
&&&&&&
−=−+−
+−+−+
++
++−
or,
.2.10…coscos
*)()(
111
11,1,
gnmmmmm
mmmmsmmmsmm
xmQQP
Pxxcxxcxm
&&
&&&&&&
−=−+−
+−+−+
+++
++−
φφ
Where mm is the mass at the story m; cs,m+1 and
cs,m are the structural damping between story m +
1 and m, and between story m and m − 1,
respectively. xm+1 , xm , and xm−1 , are designated
as the relative displacement at story m + 1, m, and
m − 1. Qm+1 and Qm are denoted as the structural
force between story m + 1 and m, and between
story m and m − 1, respectively. Pm+1 , Pm , Dm+1 ,
and Dm represent the axial force and the
horizontal component of damping devices
between story m + 1 and m, and between story m
International Journal of Advanced Engineering Technology E-ISSN 0976-3945
IJAET/Vol.II/ Issue III/July-September, 2011/
and m − 1. φ m+1 and φ m are angles between the
axial force, Pm+1 or Pm , and the horizontal
component Dm+1 or Dm of the damping devices.
Equations 2.9 and 2.9 form multiple-degree-of-
freedom (MDOF) motion equations. These
equations can be condensed in matrix notations
and symbolically shown as below:
}1]{[}1]{[}1]{[}]{[}]{[ MxQDxCxm g&&&&& −=+++ ..2.11
Where the mass matrix, [M], the structural
damping matrix, [C], the damping force matrix
[D], and the structural force matrix, [Q]. Once the
damping devices are identified and the
mechanical properties of the seismic force-
resisting system are selected, the damping force
matrix [D] and the structural force matrix [Q] can
be explicitly determined from the relation
between the damping force and the relative
velocity or displacement, as well as from the
relation between the structural force and its
deformation, respectively. Consequently, the
displacement, velocity, and acceleration of the
seismic force resisting system and the damping
system are explicitly computed from Equation
2.11 in accordance with the input of the ground
acceleration, gx&& .
3. NUMERICAL STUDY
The seismic response of 12-story model, 17-story
model, and 22-story model with different alternative
arrangement of viscous damper subjected to real
earthquake ground motion is investigated. The
response is investigated under different earthquake
ground motions as represented in Table 1. In this
report Comparative study between Buildings with
dampers, without dampers, with bracing system.
Caparison has been done for seismic response like
base shear, top floor displacement (top drift) and
acceleration. The mass at each floor is assumed to
be equal and the inherent damping of the frame is
considered 5%. SAP2000 nonlinear time history
analysis program was applied to investigate the
effects on building such as normalized base shear,
tip displacement, normalized acceleration and
energy dissipation of damper element by varying
different important parameters namely Earthquake
time histories, location of dampers, damping
coefficient, damper stiffness, no of story of building.
Figure 2.3 Mathematical Model of MDOF structures with damping devices.
International Journal of Advanced Engineering Technology E-ISSN 0976-3945
IJAET/Vol.II/ Issue III/July-September, 2011/
Table 1. Details of earthquakes considered for the numerical study
Name Magnitude
Duration of
Earthquake
(sec)
PGA *
Value
(cm/sec2)
Time for
PGA
(sec)
Type
of
E.Q.
Koyna (1967,Maharashtra, INDIA)
6.5 7.02 54.1 2.606 Short
El Centro (1940, Imperial Valley Irrigation District)
7.1 31.18 142.18 0.29 Short
Bhuj (2001,Gujarat,INDIA) 7.6 109.995 103.82 46.940 Long Tohoku, Japan (2011, Undo) 9.0 639.99 152.055 107.79 Long
*PGA – Peak Ground Acceleration
3.1 Time History Plot of Earthquake Data
For engineering purposes, the time variation of
ground acceleration is the most useful way of
defining the shaking of ground during earthquake.
This ground acceleration is descriptive by
numerical values at discrete time intervals. This
plot for Koyna, EL Centro, Bhuj and Tohoku,
Japan earthquake are shown here
.
Fig 3.1 Acceleration (mm/sec
2) Vs Time (sec) Response for Koyna Earthquake
Fig 3.2 Acceleration (mm/sec
2) Vs Time (sec) Response for EL Centro Earthquake
Fig 3.3 Acceleration (m/sec
2) Vs Time (sec) Response for Bhuj Earthquake
International Journal of Advanced Engineering Technology E-ISSN 0976-3945
IJAET/Vol.II/ Issue III/July-September, 2011/
Fig 3.4 Acceleration (mm/sec
2) Vs Time (sec) Response for Japan Earthquake
3.2 Effect on Normalized Base Shear
Figure 3.1 illustrates the Normalized Base Shear
response of the structure verses Time under the
Koyna (1967, Maharashtra) earthquake, El Centro
(1940, Imperial Valley Irrigation District), Bhuj
(2001, Gujarat) , Tohoku, Japan (2011, Undo) and
static earthquake analysis. It can be seen that in
Table 3.1 that the incorporation of the dampers
reduced the peak value of the Normalized Base. This
table is also showing that reduction in Base shear is
mainly depending on Earthquake acceleration and
No of story. These results are similar to the results
obtained for the 22-story, 17-story and 12-story
building but the percentage reduction is different for
different no of story. Figure 3.5, 3.6 and 3.7 easily
demonstrated that dampers can be used to improve
the mitigation of seismic forces. From the above
figure variation in Static analysis for base shear is
very less, which indicate the accuracy of Nonlinear
Time History method and results are very to
accurate results.
Table 3.1 Percentage reduction in Base Shear
due to Dampers.
Earthquakes 12-
Story
17-
Story
22-
Story
Koyna, 1967 18 % 43 % 25 %
El Centro, 1940 8 % 5 % 5 %
Bhuj, 2001 16 % 28 % 30 %
Tohoku, Japan, 2011 17 % 5 % 26 %
Figure 3.5 Normalized Base Shear for 22-Story
Figure 3.6 Normalized Base Shear for 17-Story
International Journal of Advanced Engineering Technology E-ISSN 0976-3945
IJAET/Vol.II/ Issue III/July-September, 2011/
Figure 3.7 Normalized Base Shear for 12-Story
3.3 Generalized Effects of Adding Damping to a
Structure
The effects of added damping in a structure
subjected to earthquake transients is depicted in the
results obtained from SAP2000 Non-linear time
history analysis provided in Figure 3.8 to 3.15. The
tested structure was a 22-story, RCC building frame.
Figure 3.8 to 3.11 shows the response of the
structure under input of the Koyna, 1940 El Centro,
Bhuj and Japan earthquake for un-damped
condition. Note that a small hysteresis loop is
apparent in Figure 3.8 to 3.11 revealing that the test
structure was at the onset of yield. In comparison,
Figure 3.12 to 3.15 is the same structure with added
damping, obtained by the addition nonlinear fluid
dampers installed as diagonal brace elements. The
large energy dissipation of added damping is readily
apparent in the “football” shaped damping curve
superimposed over the structural spring rate curve.
Fig 3.8 Energy Dissipation for Undamped for
Koyna Earthquake (22-story) Fig 3.9 Energy Dissipation for Undamped for EL
Centro Earthquake (22-story)
Fig 3.10 Energy Dissipation for Undamped for
Bhuj Earthquake (22-story)
Fig 3.11 Energy Dissipation for Undamped for
Japan Earthquake (22-story)
International Journal of Advanced Engineering Technology E-ISSN 0976-3945
IJAET/Vol.II/ Issue III/July-September, 2011/
Fig 3.12 Energy Dissipation for Damper for
Koyna Earthquake (22-story)
Fig 3.13 Energy Dissipation for Damper for EL
Centro Earthquake (22-story)
Fig 3.14 Energy Dissipation for Damper for Bhuj
Earthquake (22-story)
Fig 3.15 Energy Dissipation for Damper for
Japan Earthquake (22-story)
3.4 Effects on Base Shear and Story Drift.
It is clear that the characteristics of base shear is
completely depends on input type of Earthquake and
no of story. At very high stiffness of dampers, the
buildings behave as they are rigidly connected by
bracing. As a result, the relative displacements and the
relative velocities of the connected floors become
almost zero and the damper totally loses its
effectiveness. On the other hand, if the stiffness of
dampers is reduced to zero, the buildings return to the
unconnected condition like building without dampers
or un-damped condition, as a result dampers again
losses its effectiveness. Effectiveness of dampers is
also depends on no of storey. As no of story decreases
the overall stiffness of building increases to counter
act this thing damper stiffness was to be reduce
relative to higher no of story in this investigation.
Continuous decrease in effective stiffness of dampers
show increase in story drift as well as increased base
shear. Which clearly indicate that optimum effective
stiffness for particular no of story exist. The time
variation of the top floor displacement and base shear
responses of the 22-story buildings connected by
dampers at all the floors, is shown in Figures 3.16 to
3.23. These figures clearly indicate the effectiveness
of dampers in controlling the earthquake responses of
both the buildings. Similar types of results are
obtained for the 12-story building and 17-story
building but results for 22-story is presented over here.
Figure 3.16 Base Shear v/s Time for Koyna
Earthquake for 22 Story.
Figure 3.17 Base Shear v/s Time for El Centro for
22 Story.
International Journal of Advanced Engineering Technology E-ISSN 0976-3945
IJAET/Vol.II/ Issue III/July-September, 2011/
Figure 3.18 Base Shear v/s Time for Bhuj
Earthquake for 22 Story.
Figure 3.19 Base Shear v/s Time for Japan(2011)
Earthquake for 22 Story.
Figure 3.20 Top Drift v/s Time for Koyna
Earthquake for 22 Story.
Figure 3.21 Top Drift v/s Time for El Centro for
22 Story.
Figure 3.22 Top Drift v/s Time for Bhuj Earthquake
for 22 Story.
Figure 3.23 Top Drift v/s Time for Japan(2011)
Earthquake for 22 Story.
4. DISCUSSION AND CONCLUSION
Comparison between Building with dampers and
Building with braces showed that dampers are
more significant to reduce seismic quantities with
same direction of placement as brace. Dampers
placed in the upper levels had little to no effect on
the structural response. The responses of the
structure were compared under different
earthquake records. There were significant
reductions in deflection and acceleration response
under all earthquake records. The reduction in
acceleration will lead to lesser inertia forces and so
increases the ability of the building to cope with
seismic events. The response however, varied with
the earthquake record indicating its dependence on
the intensity and frequency content of the
earthquake. The results showed that there was a
correlation between the amount of rigidity cut out
of the system and the stiffness and damping
coefficients of the damper replacing this. This
suggests that there is a need to balance these
parameters in order to obtain the optimum
improvement in seismic performance. The
investigations showed that significant reduction in
structure acceleration, deformation and Base shear
can be achieved by strategically placing the
dampers within the periphery of structure where
twisting deformation is significant and controlling
the reduction of stiffness within a reasonable
range. Problem of optimal damper placement in a
International Journal of Advanced Engineering Technology E-ISSN 0976-3945
IJAET/Vol.II/ Issue III/July-September, 2011/
soil-structure interaction model including damper
support member systems would be of interest for
future research. Comparative investigation for
settlement of building installed with dampers and
other seismic resisting conventional frame
structure would be future work in this area.
Building installed with semi-active dampers and
active dampers would be the future investigation.
REFERENCES
• ASCE/SEI 7-05, Minimum Design Loads for Building and Other Structures, American Society of Civil Engineers (ASCE), 2005.
• Bhakararao A V, Jangid R S, Seismic Response of Adjacent Buildings Connected with Friction Dampers, Bulletin of Earthquake Engineering, 2006, Pg 43–64.
• Computer and Structures, Inc. (CSI), CSIAnalysis Reference Manual for SAP2000, ETABS, and SAFE, Berkeley, CA, 2005
• Deulkar W. N., Modhera C. D. and Patil H. S., Trends in Passive Vibration Control and Some Studies of Braced Frame, National Seminar on Earthquake Resistant Structures at SVNIT, Pg. 1-31, Sept-2010.
• Douglas P. Taylor, History, Design and Application of Fluid Dampers in Structural Engineering, Taylor Devices, 2010.
• Edward L. Wilson, Three-Dimensional Static and Dynamic Analysis of Structures A Physical Approach With Emphasis on Earthquake Engineering, Third Edition, Reprint January 2002, Pg 18-12 to 22-21
• Franklin Y. Cheng , Hongping Jiang, Kangyu Lou, SMART STRUCTURES Innovative Systems for Seismic Response Control, Taylor and Francis Group, Pg. 1-40, LLC, 2008. Pg 109 to 157
• Izuru Takewaki, Building Control with Passive Dampers, Optimal Performance-based Design of Earthquakes, John Wiley & Sons(Asia) Pte.Ltd, Singapore, 2009
• KAMURA Hisaya, NANBA Takayuki, OKI Koji, FUNABA Taku, Seismic Response Control for High-Rise Buildings Using Energy-Dissipation Devices, JFE Technical Report, No. 14, Dec. 2009.
• Kan Shimizu, Orui Satoshi, Control Effect of Hydraulic Dampers Installed in High-rise Building Observed during Earthquakes, CTBUH 8th World Congress, 2008, Pg 1-7.
• Madsen L.P.B., Thambiratnam D.P., Perera N.J., Seismic response of building structures with dampers in shear walls, Science Direct, 1 November 2002.
• Masoomi Mohammad Saeed, Osman Siti Aminah, and Shojaeipour Shahed, Modeling of Hysteretic Damper in Three-Story Steel Frame Subjected to Earthquake Load, Proceedings of the 3rd International Conference on Environmental and Geological Science and Engineering, 2009.
• Masri, S. F., Seismic Response Control of Structural System: Closure, Proceeding of Ninth World Conference of Earthquake Engineering, Tokyo-Kyoto, Vol. VIII, Pg. 497-502, 2-9 August, 1988.
• Meng-Hao Tsai and Kuo-Chun Chang, Higher-mode effect on the seismic responses of buildings with viscoelastic dampers, Earthquake Engineering and Engineering Vibration, June 2002, Pg 1-11.
• Mevada Snehal V. and Jangid R. S., Seismic Response of Building installed with Semi-active Dampers, National Seminar on Earthquake Resistant Structures at SVNIT, Pg. 1-16, Sept-2010.
• Miyamoto H. Kit, S.E. and Roger E. Scholl Fluid viscous dampers are designed to control this complex building’s response during a sesmic event, Modern Steel Construction, November 1998, Pg 1-5.
• Orlando Cundumi Sánchez, A variable damping semiactive device for control of the seismic response of building, University of Puerto Rico, Mayaguez Campus, 2005.
• Robert Levy and Oren Lavan, Fully Stressed Seismic Design of Dampers in Framed Structures, Springer, 2006, Pg 303–315.
• Safai Aliyeh Jowrkesh, Analytical Studies of a 49-Storey Eccentric Braced Building, BA.Sc. Gilan University, Iran, 1990
• Shih M-H, Sung W-P, Development of numerical modelling of analysis program for energy-dissipating behaviour of velocity dependent hydraulic damper, Indian Academy of Sciences, Oct 2010, Pg 631-647.
• Takewaki I, Optimal damper placement for planar building frames using transfer functions, Struct Multidisc Optim, 2000, Pg 280–287.
• Unal Aldemir and Deniz Guney, Vibration Control of Non-linear Building Under Seismic Loads, Springer, 2007, Pg 39-44.
• Yu-Yuan Lin, Kuo-Chun Chang , Chang-Yu Chen Direct displacement-based design for seismic retrofit of existing buildings using nonlinear viscous dampers, Springer Science, 4 March 2008, Pg 538-552.