Rashmi TMD
Rashmi TMD
Rashmi TMD
THE DEGREE OF
MASTER OF TECHNOLOGY
IN
STRUCTURAL ENGINEERING
BY
RASHMI MISHRA
209CE2044
NATIONAL INSTITUTE OF TECHNOLOGY, ROURKELA
THE DEGREE OF
MASTER OF TECHNOLOGY
IN
STRUCTURAL ENGINEERING
BY
RASHMI MISHRA
UNDER THE GUIDANCE OF
Certificate
This is to certify that the thesis entitled, APPLICATION OF TUNED MASS
DAMPER FOR VIBRATION CONTROL OF FRAME STRUCTURES UNDER
SEISMIC EXCITATIONS submitted by Rashmi Mishra in partial fulfillment of
the requirements for the award of
Master of Technology
Degree in Civil
(Prof.K.C.Biswal)
Dept. of Civil Engineering
National Institute of Technology,
Rourkela-769008
ACKNOWLEDGEMENT
I express my deepest gratitude to my project guide Prof. K.C.Biswal, whose encouragement,
guidance and support from the initial to the final level enabled me to develop an understanding
of the subject.
Besides, we would like to thank to Prof. M. Panda, Head of the Civil engineering Department,
National Institutes of Technology, Rourkela for providing their invaluable advice and for
providing me with an environment to complete our project successfully.
I am deeply indebted to Prof. S. K. Sahu, Prof. M.R. Barik, Prof. (Mrs) A.V.Asha and all
faculty members of civil engineering department, National Institutes of Technology, Rourkela,
for their help in making the project a successful one.
Finally, I take this opportunity to extend my deep appreciation to my family and friends, for all
that they meant to me during the crucial times of the completion of my project.
RASHMI MISHRA
Date: 25.05.2011
Place: Rourkela
CONTENTS:
ABSTRACT
LIST OF FIGURES
ii-iv
LIST OF TABLES
CHAPTER-1 INTRODUCTION
1-11
1.1
Introduction
1-2
1.2
2-3
1.3
3-8
3-4
4-5
7-8
8-9
Practical Implementations
9-11
1.4
1.5
12-24
2.1
Review of literature
12-24
2.2
24
25-41
3.1
25-27
3.2
27-32
3.2.1
28-30
3.2.2
30-32
3.3
32-37
3.4
37-39
3.4.1 Solution of Forced vibration problem using Newmark Beta Method 37-39
CHAPTER-4 RESULTS AND DISCUSSIONS
4.1
4.2
Shear Building
40-72
40
41-44
41-42
43-44
4.3
TMD-Structure interaction
4.3.1 Effect of TMD in structural damping when damping
45-57
45-49
49-57
4.4
58-59
4.5
Preliminary Calculations
60
4.6
61-62
4.7
4.8
61
62
63-67
63-65
65-67
68-71
72-73
5.1
Summary
72-73
5.2
73
CHAPTER-6 REFERENCES
74-82
ABSTRACT:
Current trends in construction industry demands taller and lighter structures, which are also more
flexible and having quite low damping value. This increases failure possibilities and also
problems from serviceability point of view. Now-a-days several techniques are available to
minimize the vibration of the structure, out of the several techniques available for vibration
control ,concept of using TMD is a newer one. This study was made to study the effectiveness of
using TMD for controlling vibration of structure. At first a numerical algorithm was developed
to investigate the response of a shear building fitted with a TMD. Then another numerical
algorithm was developed to investigate the response of a 2D frame model fitted with a TMD. A
total of three loading conditions were applied at the base of the structure. First one was a
sinusoidal loading, the second one was corresponding to compatible time history as per spectra
of IS-1894 (Part -1):2002 for 5% damping at rocky soil with (PGA = 1g) and the third one was
1940 El Centro Earthquake record with (PGA = 0.313g).
From the study it was found that, TMD can be effectively used for vibration control of
structures. TMD was more effective when damping ratio of the structure is less. Gradually
increasing the mass ratio of the TMD results in gradual decrement in the displacement response
of the structure.
RASHMI MISHRA
ROLL NO: 209CE2044
Date: 24.05.2011
Place: Rourkela
LIST OF FIGURES
25
28
30
TMD system.
3.4Undamped SDOF system coupled with a damped
33
TMD system.
3.5 Co-ordinate transformation for 2D frame elements
37
39
41
42
43
44
46
Structure
4.6 Amplitude of vibration at top storey by placing TMD at
48
52
56
storey with the variation of the mass ratio of the TMD when,
El Centro(1940) earthquake loading acting on the structure.
4.9 Elevation of 2D plane frame structure
58
61
64
65
66
67
69
iv
70
LIST OF TABLES
60
61
CHAPTER-1
INTRODUCTION
1.1 Introduction
Vibration control is having its roots primarily in aerospace related problems such as tracking
and pointing, and in flexible space structures, the technology quickly moved into civil
engineering and infrastructure-related issues, such as the protection of buildings and bridges
from extreme loads of earthquakes and winds.
The number of tall buildings being built is increasing day by day. Today we cannot have a
count of number of low-rise or medium rise and high rise buildings existing in the world.
Mostly these structures are having low natural damping. So increasing damping capacity of
a structural system, or considering the need for other mechanical means to increase
the damping capacity of a building, has become increasingly common in the new
generation of tall and super tall buildings. But, it should be made a routine design practice
to design the damping capacity into a structural system while designing the structural system.
The control of structural vibrations produced by earthquake or wind can be done by various
means such as modifying rigidities, masses, damping, or shape, and by providing passive or
active counter forces. To date, some methods of structural control have been used
successfully and newly proposed methods offer the possibility of extending applications and
improving efficiency.
The selection of a particular type of vibration control device is governed by a number of
factors which include efficiency, compactness and weight, capital cost, operating cost,
maintenance requirements and safety.
Tuned mass dampers (TMD) have been widely used for vibration control in mechanical
engineering systems. In recent years, TMD theory has been adopted to reduce
vibrations of tall buildings and other civil engineering structures. Dynamic absorbers
and tuned mass dampers are the realizations of tuned absorbers and tuned dampers for
structural vibration control applications. The inertial, resilient, and dissipative elements in
such devices are: mass, spring and dashpot (or material damping) for linear applications and
their rotary counterparts in rotational applications. Depending on the application, these
devices are sized from a few ounces (grams) to many tons. Other configurations such as
pendulum absorbers/dampers, and sloshing liquid absorbers/dampers have also been realized
for vibration mitigation applications.
TMD is attached to a structure in order to reduce the dynamic response of the structure. The
frequency of the damper is tuned to a particular structural frequency so that when that
frequency is excited, the damper will resonate out of phase with the structural motion. The
mass is usually attached to the building via a spring-dashpot system and energy is
dissipated by the dashpot as relative motion develops between the mass and the
structure.
Passive energy dissipation systems utilises a number of materials and devices for enhancing
damping, stiffness and strength, and can be used both for natural hazard mitigation and for
rehabilitation of aging or damaged structures. In recent years, efforts have been undertaken to
develop the concept of energy dissipation or supplemental damping into a workable
technology and a number of these devices have been installed in structures throughout the
world (Soong and Constantinou 1994; Soong and Dargush 1997). In general, they are
characterized by the capability to enhance energy dissipation in the structural systems in
which they are installed. This may be achieved either by conversion of kinetic energy to heat,
or by transferring of energy among vibrating modes. The first method includes devices that
operate on principles such as frictional sliding, yielding of metals, phase transformation in
metals, deformation of viscoelastic solids or fluids, and fluid orificing. The later method
includes supplemental oscillators, which act as dynamic vibration absorbers.
the damper elements utilizing the friction principle, which can be installed in a structure in an
X-braced frame as illustrated in the figure (Palland Marsh 1982).
Tuned liquid column dampers (TLCDs) are a special type of tuned liquid damper (TLD) that
rely on the motion of the liquid column in a U-shaped tube to counter act the action of
external forces acting on the structure. The inherent damping is introduced in the oscillating
liquid column through an orice.
The performance of a single-degree-of-freedom structure with a TLD subjected to sinusoidal
excitations was investigated by Sun(1991), along with its application to the suppression of
wind induced vibration by Wakahara et al. (1989). Welt and Modi (1989) were one of the
first to suggest the usage of a TLD in buildings to reduce overall response during strong wind
or earthquakes.
the crown of the structure, has a mass of 366 Mg, about 2% of the effective modal mass of
the first mode, and was 250 times larger than any existing tuned mass damper at the time of
installation. Designed to be bi-axially resonant on the building structure with a variable
operating period of , adjustable linear damping from 8 to 14%, and a peak relative
displacement of , the damper is expected to reduce the building sway amplitude by about
50%.
Two dampers were added to the 60-storey John Hancock Tower in Boston to reduce the
response to wind loading. The dampers are placed at opposite ends of the fifty-eighth story,
67 m apart, and move to counteract sway as well as twisting due to the shape of the building.
Each damper weighs 2700 kN and consists of a lead-filled steel box about 5.2 m square and 1
m deep that rides on a 9-m-long steel plate. The lead-filled weight, laterally restrained by stiff
springs anchored to the interior columns of the building and controlled by servo-hydraulic
cylinders, slides back and forth on a hydrostatic bearing consisting of a thin layer of oil
forced through holes in the steel plate.
Chiba Port Tower (completed in 1986) was the first tower in Japan to be equipped with a
TMD. Chiba Port Tower is a steel structure 125 m high weighing 1950 metric tons and
having a rhombus-shaped plan with a side length of 15 m. The first and second mode periods
are 2.25 s and 0.51 s, respectively for the x direction and 2.7 sand 0.57 s for the y direction.
Damping for the fundamental mode is estimated at 0.5%. Damping ratios proportional to
frequencies were assumed for the higher modes in the analysis. The purpose of the TMD is to
increase damping of the first mode for both the x and y directions. the damper has mass ratios
with respect to the modal mass of the first mode of about 1/120 in the x direction and 1/80 in
the y direction; periods in the x and y directions of 2.24 s and 2.72 s, respectively; and a
damper damping ratio of 15%. The maximum relative displacement of the damper with
10
respect to the tower is about in each direction. Reductions of around 30 to 40% in the
displacement of the top floor and 30% in the peak bending moments are expected.
In Japan, counter measures against traffic-induced vibration were carried out for two twostory steel buildings under an urban expressway viaduct by means of TMDs (Inoue et
al.1994). Results show that peak values of the acceleration response of the two buildings
were reduced by about 71% and 64%, respectively, by using the TMDs with the mass ratio
about 1%.
11
CHAPTER-2
LITERATURE REVIEW
2.1) Review of Literature
. The TMD concept was first applied by Frahm in 1909 (Frahm, 1909) to reduce the rolling
motion of ships as well as ship hull vibrations. A theory for the TMD was presented later in
the paper by Ormondroyd and Den Hartog(1928),followed by a detailed discussion of
optimal tuning and damping parameters in Den Hartogs book on mechanical vibrations
(1940).Hartogs book on mechanical vibrations (1940). The initial theory was applicable
foran undamped SDOF system subjected to a sinusoidal force excitation. Extension of the
theory to damped SDOF systems has been investigated by numerous researchers.
Active control devices operate by using an external power supply. Therefore ,they are more
efficient than passive control devices. However the problems such as insufficient controlforce capacity and excessive power demands encountered by current technology in the
context of structural control against earthquakes are unavoidable and need to be overcome.
Recently a new control approach-semi-active control devices, which combine the best
features of both passive and active control devices, is very attractive due to their low power
demand and inherent stability. The earlier papers involving SATMDs may traced to 1983.
Hrovat et al.(1983) presented SATMD, a TMD with time varying controllable damping.
Under identical conditions, the behaviour of a structure equipped with SATMD instead of
TMD is significantly improved. The control design of SATMD is less dependent on related
parameters (e.g, mass ratios, frequency ratios and so on), so that there greater choices in
selecting them.
12
The first mode response of a structure with TMD tuned to the fundamental frequency of the
structure can be substantially reduced but, in general, the higher modal responses may only
be marginally suppressed or even amplified. To overcome the frequency-related limitations
of TMDs, more than one TMD in a given structure, each tuned to a different dominant
frequency, can be used. The concept of multiple tuned mass dampers (MTMDs) together with
an optimization procedure was proposed by Clark (1988). Since, then, a number of studies
have been conducted on the behaviour of MTMDs a doubly tuned mass damper (DTMD),
consisting of two masses connected in series to the structure was proposed (Setareh 1994). In
this case, two different loading conditions were considered: harmonic excitation and zeromean white-noise random excitation, and the efficiency of DTMDs on response reduction
was evaluated. Analytical results show that DTMDs are more efficient than the conventional
single mass TMDs over the whole range of total mass ratios, but are only slightly more
efficient than TMDs over the practical range of mass ratios (0.01-0.05).
Recently, numerical and experimental studies have been carried out on the effectiveness of
TMDs in reducing seismic response of structures [for instance, Villaverde(1994)]. In
Villaverde(1994), three different structures were studied, in which the first one is a 2D two
story shear building the second is a three-dimensional (3D) one-story frame building, and the
third is a 3D cable-stayed bridge, using nine different kinds of earthquake records. Numerical
and experimental results show that the effectiveness of TMDs on reducing the response of the
same structure during different earthquakes, or of different structures during the same
earthquake is significantly different; some cases give good performance and some have little
or even no effect. This implies that there is a dependency of the attained reduction in
response on the characteristics of the ground motion that excites the structure. This response
reduction is large for resonant ground motions and diminishes as the dominant frequency of
13
the ground motion gets further away from the structure's natural frequency to which the TMD
is tuned. Also, TMDs are of limited effectiveness under pulse-like seismic loading.
Multiple passive TMDs for reducing earthquake induced building motion. Allen J. Clark
(1988). In this paper a methodology for designing multiple tuned mass damper for reducing
building response motion has been discussed. The technique is based on extending Den
Hartog work from a single degree of freedom to multiple degrees of freedom. Simplified
linear mathematical models were excited by 1940 El Centro earthquake and significant
motion reduction was achieved using the design technique.
Performance of tuned mass dampers under wind loads K. C. S. Kwok et al(1995).The
performance of both passive and active tuned mass damper (TMD) systems can be
readily assessed by parametric studies which have been the subject of numerous
research.. Few experimental verifications of TMD theory have been carried out,
particularly those involving active control, but the results of those experiments generally
compared well with those obtained by parametric studies. Despite some serious design
constraints, a number of passive and active tuned mass damper systems have been
successfully installed in tall buildings and other structures to reduce the dynamic
response due to wind and earthquakes.
Mitigation of response of high-rise structural systems by means of optimal tuned mass
damper. A.N Blekherman(1996). In this paper a passive vibration absorber has been proposed
to protect high-rise structural systems from earthquake damages. A structure is modelled by
one-mass and n-mass systems(a cantilever scheme). Damping of the structure and absorber
installed on top of it is represented by frequency independent one on the base of equivalent
visco-elastic model that allows the structure with absorber to be described as a system with
non-proportional internal friction. A ground movement is modelled by an actuator that
14
produces vibration with changeable amplitude and frequency. To determine the optimum
absorber parameters, an optimization problem, that is a minmax one , was solved by using
nonlinear programming technique( the Hooke-Jeves method).
Survey of actual effectiveness of mass damper systems installed in buildings. T.Shimazu and
H.Araki(1996). In this paper the real state of the implementation of mass damper systems, the
effects of these systems were clarified based on various recorded values in actual buildings
against both wind and earthquake. The effects are discussed in relation with the natural
period of buildings equipped with mass damper systems, the mass weight ratios to building
weight, wind force levels and earthquake ground motion levels.
A method of estimating the parameters of tuned mass dampers for seismic applications.
Fahim Sadek et al(1997). In this paper the optimum parameters of TMD that result in
considerable reduction in the response of structures to seismic loading has been presented.
The criterion that has been used to obtain the optimum parameters is to select for a given
mass ratio, the frequency and damping ratios that would result in equal and large modal
damping in the first two modes of vibration. The parameters are used to compute the response
of several single and multi-degree of freedom structures with TMDs to different earthquake
excitations. The results show that the use of the proposed parameters reduces the
displacement and acceleration responses significantly. The method can also be used for
vibration control of tall buildings using the so-called mega-substructure configuration,
where substructures serve as vibration absorbers for the main structure.
Structural control: past, present, and future G. W. Housner et al(1996).This paper basically
provides a concise point of departure for those researchers and practitioners who wishing to
assess the current state of the art in the control and monitoring of civil engineering structures;
and provides a link between structural control and other fields of control theory, pointing out
15
both differences and similarities, and points out where future research and application efforts
are likely to prove fruitful.
Structural vibration of tuned mass installed three span steel box bridge. Byung-Wan Jo et al
(2001).To reduce the structural vibration of a three span steel box bridge a three axis two
degree of freedom system is adopted to model the mass effect of the vehicle; and the kinetic
equation considering the surface roughness of the bridge is derived based on Bernoulli-Euler
beam ignoring the torsional DOF. The effects of TMD on steel box bridge shows that it is not
effective in reducing the maximum deflection ,but it efficiently reduces the free vibration of
the bridge. It proves that the TMD is effective in controlling the dynamic amplitude rather
than the maximum static deflection.
Optimal placement of multiple tuned mass dampers for seismic structures. Genda Chen et
al(2001). In this paper effects of a tuned mass damper on the modal responses of a six-story
building structure are studied. Multistage and multimode tuned mass dampers are then
introduced. Several optimal location indices are dened based on intuitive reasoning, and a
sequential procedure is proposed for practical design and placement of the dampers in
seismically excited building structures. The proposed procedure is applied to place the
dampers on the oors of the six-story building for maximum reduction of the accelerations
under a stochastic seismic load and 13 earthquake records. Numerical results show that the
multiple dampers can effectively reduce the acceleration of the uncontrolled structure by 10
25% more than a single damper. Time-history analyses indicate that the multiple dampers
weighing 3% of total structural weight can reduce the oor acceleration up to 40%.
Seismic effectiveness of tuned mass dampers for damage reduction of structures. T. Pinkaew
et al(2002).The effectiveness of TMD using displacement reduction of the structure is found
to be insufcient after yielding of the structure, damage reduction of the structure is proposed
16
(PMCLD) treatments; and developing innovative surface damping treatments using microcellular foams and active standoff constrained layer (ASCL) treatments. The results obtained
from the above and several other vibration suppression oriented research projects being
carried out under the ARO sponsorship are also included in this study.
Performance of a ve-storey benchmark model using an active tuned mass damper and a
fuzzy controller. Bijan Samali, Mohammed Al-Dawod(2003). This paper describes the
performance of a ve-storey benchmark model using an active tuned mass damper (ATMD),
where the control action is achieved by a Fuzzy logic controller (FLC) under earthquake
excitations. The advantage of the Fuzzy controller is its inherent robustness and ability to
handle any non-linear behaviour of the structure. The simulation analysis of the ve-storey
benchmark building for the uncontrolled building, the building with tuned mass damper
(TMD), and the building with ATMD with Fuzzy and linear quadratic regulator (LQR)
controllers has been reported, and comparison between Fuzzy and LQR controllers is made.
In addition, the simulation analysis of the benchmark building with different values of
frequency ratio, using a Fuzzy controller is conducted and the effect of mass ratio, on the
ve-storey benchmark model using the Fuzzy controller has been studied.
Behaviour of soil-structure system with tuned mass dampers during near-source earthquakes.
Nawawi Chouw(2004). In this paper the influence of a tuned mass damper on the behaviour
of a frame structure during near-source ground excitations has been presented. In the
investigation the effect of soil-structure interaction is considered, and the natural frequency of
the tuned mass damper is varied. The ground excitations used are the ground motion at the
station SCG and NRG of the 1994 Northridge earthquake. The investigation shows that the
soil-structure interaction and the characteristic of the ground motions may have a strong
influence on the effectiveness of the tuned mass damper. But in order to obtain a general
conclusion further investigations are necessary.
18
Wind Response Control of Building with Variable Stiffness Tuned Mass Damper Using
Empirical Mode Decomposition Hilbert Transform Nadathur Varadarajan et al(2004).The
effectiveness of a novel semi-active variable stiffness-tuned mass damper ~SAIVS-TMD! for
the response control of a wind-excited tall benchmark building is investigated in this study.
The benchmark building considered is a proposed 76-story concrete ofce tower in
Melbourne, Australia. Across wind load data from wind tunnel tests are used in the present
study. The objective of this study is to evaluate the new SAIVS-TMD system, that has the
distinct advantage of continuously retuning its frequency due to real time control and is
robust to changes in building stiffness and damping. The frequency tuning of the SAIVSTMD is achieved based on empirical mode decomposition and Hilbert transform
instantaneous frequency algorithm developed by the writers. It is shown that the SAIVSTMD can reduce the structural response substantially, when compared to the uncontrolled
case, and it can reduce the response further when compared to the case with TMD.
Additionally, it is shown the SAIVS-TMD reduces response even when the building stiffness
changes by
15%.
Effect of soil interaction on the performance of tuned mass dampers for seismic applications.
A. Ghosha, B. Basu(2004).The properties of the structure used in the design of the TMD are
those evaluated considering the structure to be of a xed-base type. These properties of the
structure may be signicantly altered when the structure has a exible base, i.e. when the
foundation of the structure is supported on compliant soil and undergoes motion relative to
the surrounding soil. In such cases, it is necessary to study the effects of soil-structure
interaction (SSI) while designing the TMD for the desired vibration control of the structure.
In this paper, the behaviour of exible-base structures with attached TMD, subjected to
earthquake excitations has been investigated. Modied structural properties due to SSI has
been covered in this paper.
19
Optimal design theories and applications of tuned mass dampers. Chien-Liang Lee et
al(2006).An optimal design theory for structures implemented with tuned mass dampers
(TMDs) is proposed in this paper. Full states of the dynamic system of multiple-degree-offreedom (MDOF) structures, multiple TMDs (MTMDs) installed at different stories of the
building, and the power spectral density (PSD) function of environmental disturbances are
taken into account. The optimal design parameters of TMDs in terms of the damping
coefcients and spring constants corresponding to each TMD are determined through
minimizing a performance index of structural responses dened in the frequency domain.
Moreover, a numerical method is also proposed for searching for the optimal design
parameters of MTMDs in a systematic fashion such that the numerical solutions converge
monotonically and effectively toward the exact solutions as the number of iterations
increases. The feasibility of the proposed optimal design theory is veried by using a SDOF
structure with a single TMD (STMD), a ve-DOF structure with two TMDs, and a ten-DOF
structure with a STMD.
Optimum design for passive tuned mass dampers using viscoelastic materials. I Saidi, A D
Mohammed et al(2007). This paper forms part of a research project which aims to develop
an innovative cost effective Tune Mass Damper (TMD) using viscoelastic materials.
Generally, a TMD consists of a mass, spring, and dashpot which is attached to a floor to
form a two-degree of freedom system. TMDs are typically effective over a narrow
frequency band and must be tuned to a particular natural frequency. The paper
provides a detailed methodology for estimating the required parameters for an optimum
TMD for a given floor system. The paper also describes the process for estimating the
equivalent viscous damping of a damper made of viscoelastic material. Finally, a new
innovative prototype viscoelastic damper is presented along with associated preliminary
results.
20
Semi-active Tuned Mass Damper for Floor Vibration Control .Mehdi Setareh et al(2007). A
semi-active magneto-rheological device is used in a pendulum tuned mass damper PTMD
system to control the excessive vibrations of building oors. This device is called semi-active
pendulum tuned mass damper SAPTMD. Analytical and experimental studies are conducted
to compare the performance of the SAPTMD with its equivalent passive counterpart. An
equivalent single degree of freedom model for the SAPTMD is developed to derive the
equations of motion of the coupled SAPTMD-oor system. A numerical integration
technique is used to compute the oor dynamic response, and the optimal design parameters
of the SAPTMD are found using an optimization algorithm. Effects of off-tuning due to the
variations of the oor mass on the performance of the PTMD and SAPTMD are studied both
analytically and experimentally. From this study it can be concluded that for the control laws
considered here an optimum SAPTMD performs similarly to its equivalent PTMD, however,
it is superior to the PTMD when the oor is subjected to off-tuning due to oor mass
variations from sources other than human presence.
Seismic Energy Dissipation of Inelastic Structures with Tuned Mass Dampers. K. K. F.
Wong(2008).The energy transfer process of using a tuned mass damper TMD in improving
the ability of inelastic structures to dissipate earthquake input energy is investigated. Inelastic
structural behaviour is modelled by using the force analogy method, which is the backbone of
analytically characterizing the plastic energy dissipation in the structure. The effectiveness of
TMD in reducing energy responses is also studied by using plastic energy spectra for various
structural yielding levels. Results show that the use of TMD enhances the ability of the
structures to store larger amounts of energy inside the TMD that will be released at a later
time in the form of damping energy when the response is not at a critical state, thereby
increasing the damping energy dissipation while reducing the plastic energy dissipation. This
21
reduction of plastic energy dissipation relates directly to the reduction of damage in the
structure.
Dynamic analysis of space structures with multiple tuned mass dampers. Y.Q. Guo,
W.Q.Chen(2008). Formulations of the reverberation matrix method (RMM) are presented for
the dynamic analysis of space structures with multiple tuned mass dampers (MTMD). The
theory of generalized inverse matrices is then employed to obtain the frequency response of
structures with and without damping, enabling a uniform treatment at any frequency,
including the resonant frequency. For transient responses, the Neumann series expansion
technique as suggested in RMM is found to be conned to the prediction of accurate response
at an early time. The articial damping technique is employed here to evaluate the medium
and long time response of structures. The free vibration, frequency response, and transient
response of structures with MTMD are investigated by the proposed method through several
examples. Numerical results indicate that the use of MTMD can effectively alter the
distribution of natural frequencies as well as reduce the frequency/transient responses of the
structure. The high accuracy, lower computational cost, and uniformity of formulation of
RMM are also highlighted in this paper.
Exploring the performance of a nonlinear tuned mass damper. Nicholas A. Alexander, Frank
Schilder (2009).In this the performance of a nonlinear tuned mass damper (NTMD), which is
modelled as a two degree of freedom system with a cubic nonlinearity has been covered. This
nonlinearity is physically derived from a geometric conguration of two pairs of springs. The
springs in one pair rotate as they extend, which results in a hardening spring stiffness. The
other pair provides a linear stiffness term. In this paper an extensive numerical study of
periodic responses of the NTMD using the numerical continuation software AUTO has been
done. Two techniques have been employed for searching the optimal design parameters;
22
optimization of periodic solutions and parameter sweeps. In this paper the writers have
discovered a family of resonance curves for vanishing linear spring stiffness
Application of semi-active control strategies for seismic protection of buildings with MR
dampers. Maryam Bitaraf et al(2010).Magneto-rheological (MR) dampers are semi-active
devices that can be used to control the response of civil structures during seismic loads. They
are capable of offering the adaptability of active devices and stability and reliability of
passive devices. One of the challenges in the application of the MR dampers is to develop an
effective control strategy that can fully exploit the capabilities of the MR dampers. This study
proposes two semi-active control methods for seismic protection of structures using MR
dampers. The first method is the Simple Adaptive Control method which is classified as a
direct adaptive control method. The controller developed using this method can deal with the
changes that occur in the characteristics of the structure because it can modify its parameters
during the control procedure. The second controller is developed using a genetic-based fuzzy
control method. In particular, a fuzzy logic controller whose rule base determined by a multiobjective genetic algorithm is designed to determine the command voltage of MR dampers.
Vibration control of seismic structures using semi-active friction multiple tuned mass
dampers. Chi-Chang Lin et al.(2010) There is no difference between a friction-type tuned
mass damper and a dead mass added to the primary structure if static friction force inactivates
the mass damper. To overcome this disadvantage, this paper proposes a novel semi-active
friction-type multiple tuned mass damper (SAF-MTMD) for vibration control of seismic
structures. Using variable friction mechanisms, the proposed SAF-MTMD system is able to
keep all of its mass units activated in an earthquake with arbitrary intensity. A comparison
with a system using passive friction-type multiple tuned mass dampers (PF-MTMDs)
demonstrates that the SAF-MTMD effectively suppresses the seismic motion of a structural
23
system, while substantially reducing the strokes of each mass unit, especially for a larger
intensity earthquake.
24
CHAPTER-3
MATHEMATICAL FORMULATIONS
3.1) Concept of tuned mass damper using two mass system
The equation of motion for primary mass as shown in figure 3.1 is:
(1+ )
u=
= k/m , C = 2
m, Cd = 2 wdmd
where , is the velocity, is the acceleration, is the damping factor of the primary mass
d d d
2
d ud =
25
The purpose of adding the mass damper is to control the vibration of the structure when it is
subjected to a particular excitation. The mass damper is having the parameters; the mass md,
stiffness kd, and damping coefficient cd. The damper is tuned to the fundamental frequency of
the structure such that
d=
kd = k
The primary mass is subjected to the following periodic sinusoidal excitation
p = sint
then the response is given by
u = sin(t +1)
ud = dsin(t +1+2)
where and denote the displacement amplitude and phase shift, respectively.
The critical loading scenario is the resonant condition, The solution for this
case has the following form:
d = (1/2 d)
tan 1 =-(2 / + 1/2 d)
tan 2= - /2
26
....................................(1)
The above expression shows that the response of the tuned mass is 90 out of phase with the
response of the primary mass. This difference in phase produces the energy dissipation
contributed by the damper inertia
= ( )
1=
To compare these two cases, we can express Eq (1) in terms of an equivalent damping ratio:
(1/2 e)
where
Equation (2) shows the relative contribution of the damper parameters to the total damping.
Increasing the mass ratio magnifies the damping. However, since the added mass also
increases, so there is a practical limit on it.
27
Fig 3.3 Undamped SDOF system coupled with a damped TMD system.
Figure shows a SDOF system having mass m and stiffness k , subjected to both external
forcing and ground motion. A tuned mass damper with mass md and stiffness kd is attached to
the primary mass. The various displacement measures are ug the absolute ground motion; ,the
relative motion between the primary mass and the ground u; and ud, the relative displacement
between the damper and the primary mass.
The equations for secondary mass and primary mass are as follows:
md( d+ )+kdud= -mdag..(3)
m + ku-kdud= -mag + p(4)
where ag is the absolute ground acceleration and p is the loading applied to the primary mass .
The excitation applied on the primary mass is considered to be periodic of frequency ,
ag= gsint
p= sint
28
= = /
d= /
d=
/ kd/md
Selecting appropriate combination of the mass ratio and damper frequency ratio such that
2d+ = 0.................................................................(5)
reduces the solution to
= /k
29
d = -( /kd) 2 +( m g/kd)
.A typical range for is 0.01 to 0.1.Then the optimal damper frequency is very close to the
forcing frequency. The exact relationship follows from Eq. (5)
= / 1+
d opt
opt
=[
dopt]
md =(2 m )/(1+ )
...............................................................(8)
............................................................(9)
30
where the response amplitudes, u and ud, are considered as complex quantities. Substituting
Eqn (8) and (9) in the equations (6) and (7) and cancelling
following equations
[- md2 + icd + kd ] d -md2 = -md g
-[ icd +kd] d+ [-m2 + k] = -m g+
The solution of the governing equations is
= /kD2[f2- 2 + i2 df] - gm/k D2[(1+ )f2 -2 + i2
df(1+ )]
Fig 3.4 Undamped SDOF system coupled with a damped TMD system.
d = ( 2/k D2) ( gm/ k D2)
Where
D2= [1 -2][f2-2] - 2f2 + i2 df[1-2(1+ )]
31
f=
= H1
gm/k)H2
d= H3
- gm/k)H4
where the H factors define the amplification of the pseudo-static responses, and the s are
the phase angles between the response and the excitation. The various H terms are as follows
H1=
[f2-2]2 + [ 2 df]2) |
H2=
H3=2/|
H4=1/|
|
|
|
)])2
33
a) Element Matrices:
The element stiffness matrix for a frame structure is given by:
[k] =
Where
E = Youngs Modulus of the frame element.
A = Cross sectional area of the element.
L = Length of the element.
The element mass matrix for a frame structure is given by:
[m]=
[
34
Assuming that the local nodes 1 and 2 correspond to the global nodes i and j,respectively.
Let T be the transformation matrix for the frame element given by
35
[T] =
Where,
= cos( x , X) = cos =
= cos( x , Y) = sin =
= cos( y , Y) = cos =
Here,
= the angle between x-axis and the X-X axis as shown in the figure
=
Using the transformation matrix, T, the matrices for the frame element in the global
coordinate system become
Ke= TT kT
Me= TT mT
36
considered,
[Mf]t+t { } + [Kf]t+t {P} = {Fel}t+t
The algorithm of the scheme is highlighted below:
Initial calculations:
1)Formulation of Global Stiffness matrix K and Mass matrix M
2)Initialization of P and
3)Selection of time step t and parameters and
and 0.25(0.5+ )2
Pt+t = t+t
3) Calculation of time derivatives of pressure (P) at time t+t
t+t = a0(Pt+t - Pt) - a2 t - a3 t
and
t+t = t + a6 t + a7 t+t
39
CHAPTER-4
RESULTS AND DISCUSSIONS
4.1) Shear building:
22360.6 106N/m2
3500 mm
250 mm
40
450 mm
1
0.8
0.6
Acceleration(g)
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
10
15
20
time(sec)
25
30
35
40
a) Compatible time history as per spectra of IS-1894 (Part -1):2002 for 5% damping at
rocky soil
41
0.3
0.2
Acceleration(g)
0.1
-0.1
-0.2
-0.3
-0.4
10
15
20
time(sec)
25
30
42
35
Displacement Vs Time
0.15
0.1
Displacement
0.05
-0.05
-0.1
-0.15
-0.2
10
15
20
time
25
30
35
40
Fig 4.3a) Response of shear building to Compatible time history as per spectra of IS-1894
(Part -1):2002 for 5% damping at rocky soil
43
Displacement Vs Time
0.05
0.04
Displacement
0.03
0.02
0.01
0
-0.01
-0.02
-0.03
10
15
20
25
30
35
time
44
to 5 .
45
while the
0.15
disp without TMD
disp with TMD
0.1
Displacement(m)
0.05
-0.05
-0.1
-0.15
-0.2
10
15
20
Time(sec)
25
30
35
40
Fig 4.5 a) Response of the structure when damping ratio of the structure is 2
46
0.15
disp without TMD
disp with TMD
0.1
Displacement(m)
0.05
-0.05
-0.1
-0.15
-0.2
10
15
20
Time(sec)
25
30
35
40
Fig 4.5 b) Response of the structure when damping ratio of the structure is 5
Fig 4.5 Amplitude of vibration at top storey by placing TMD at top storey with variation of
damping ratio of the structure when corresponding to compatible time history as per spectra
of IS-1894(Part-1):2002 for 5
47
0.05
disp without TMD
disp with TMD
0.04
Displacement(m)
0.03
0.02
0.01
0
-0.01
-0.02
-0.03
10
15
20
Time(sec)
25
30
35
Fig 4.6 a) Response of the structure when damping ratio of the structure is 2
48
0.04
disp without TMD
disp with TMD
0.03
Displacement(m)
0.02
0.01
-0.01
-0.02
-0.03
10
15
20
Time(sec)
25
30
35
Fig 4.6 b) Response of the structure when damping ratio of the structure is 5
Fig 4.6 Amplitude of vibration at top storey by placing TMD at top storey with variation of
damping ratio of the structure when, El Centro (1940) earthquake loading acting on the
structure.
From the above figures it can be concluded that TMD is more effective in reducing the
displacement responses of structures with low damping ratios (2 ). But, it is less effective
for structures with high damping ratios(5 ).
49
earthquake loads.
0.15
disp without TMD
disp with TMD
mass ratio=0.3
0.1
Displacement(m)
0.05
-0.05
-0.1
-0.15
-0.2
10
15
20
Time(sec)
25
30
35
40
Fig 4.7 a) Response of the structure with TMD with 0.3 mass ratio
50
0.15
disp without TMD
disp with TMD
mass ratio=0.4
0.1
Displacement(m)
0.05
-0.05
-0.1
-0.15
-0.2
10
15
20
Time(sec)
25
30
35
40
Fig 4.7 b) Response of the structure with TMD with 0.4 mass ratio
51
0.15
disp without TMD
disp with TMD
mass ratio=0.5
0.1
Displacement(m)
0.05
-0.05
-0.1
-0.15
-0.2
10
15
20
Time(sec)
25
30
35
40
Fig 4.7 c) Response of the structure with TMD with 0.5 mass ratio
52
0.15
disp without TMD
disp with TMD
mass ratio=0.6
0.1
Displacement(m)
0.05
-0.05
-0.1
-0.15
-0.2
10
15
20
Time(sec)
25
30
35
40
Fig 4.7 d) Response of the structure with TMD with 0.6 mass ratio
Fig 4.7) Amplitude of vibration at top storey by placing TMD at top storey with variation of
mass ratio of the TMD when corresponding to compatible time history as per spectra of IS1894(Part-1):2002 for 5
53
0.04
mass ratio=0.3
0.03
Displacement(m)
0.02
0.01
-0.01
-0.02
-0.03
10
15
20
Time(sec)
25
30
35
Fig 4.8 a) Response of the structure with TMD with 0.3 mass ratio
54
0.04
mass ratio=0.4
0.03
Displacement(m)
0.02
0.01
-0.01
-0.02
-0.03
10
15
20
Time(sec)
25
30
35
Fig 4.8 b) Response of the structure with TMD with 0.4 mass ratio
55
0.04
mass ratio=0.5
0.03
Displacement(m)
0.02
0.01
-0.01
-0.02
-0.03
10
15
20
Time(sec)
25
30
35
Fig 4.8 c) Response of the structure with TMD with 0.5 mass ratio
56
0.04
disp without TMD
disp with TMD
mass ratio=0.6
0.03
Displacement(m)
0.02
0.01
-0.01
-0.02
-0.03
10
15
20
Time(sec)
25
30
35
Fig 4.8 d) Response of the structure with TMD with 0.6 mass ratio
Fig 4.8 Amplitude of vibration at top storey by placing TMD at top storey with the variation
of the mass ratio of the TMD when, El Centro(1940) earthquake loading acting on the
structure.
It can be concluded from the above graphs that increasing the mass ratio of the TMD
decreases the displacement response of the structure.
57
58
2) Size of columns
0.250 m
450m
3) Size of beams
4) Depth of slab
0.100 mm
5) Modulus of elasticity
22360.6 106N/m2
59
2) MOI of Beam
= 0.25 0.43/12
= 1.33
b)Weight of slab
=5 3.5 1000 N
= 17500 N
=2500+12500+17500 N=32500 N
60
No of elements
30
45
60
75
90
1st
13.424
13.424
13.424
13.424
13.424
2nd
43.513
43.511
43.510
43.510
43.510
3rd
81.725
81.709
81.706
81.704
81.704
4th
126.600
126.545
126.532
126.527
126.525
5th
167.534
167.015
166.924
166.899
166.889
61
No of storeys
1
1st
86.433
39.970
25.113
18.125
14.102
2nd
230.385
135.935
85.117
59.917
45.708
3rd
552.9759
213.111
159.087
113.867
85.832
4th
592.899
257.433
207.109
171.342
132.918
5th
788.338
470.714
237.3117
196.733
175.321
18
16
14
12
10
8
6
4
2
0
-0.015
-0.01
-0.005
0.005
0.01
Fig 4.10 First four mode shapes for the frame structure
62
0.015
-4
x 10
4
3
Displacement(m)
2
1
0
-1
-2
-3
-4
-5
5
time(sec)
10
-3
x 10
Velocity(m/s)
-1
-2
-3
5
time(sec)
64
10
0.02
0.015
Acceleration(m/(sec*sec))
0.01
0.005
0
-0.005
-0.01
-0.015
-0.02
5
time(sec)
10
65
0.08
0.06
Displacement(m)
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
10
15
20
time(sec)
25
30
35
40
Fig 4.12 a) Response of the frame structure to Compatible time history as per spectra of IS1894 (Part -1):2002 for 5% damping at rocky soil.
66
0.03
0.02
Displacement(m)
0.01
-0.01
-0.02
-0.03
10
15
20
time(sec)
25
30
35
67
68
0.05
disp without TMD
disp with TMD
0.04
0.03
Displacement(m)
0.02
0.01
0
-0.01
-0.02
-0.03
-0.04
-0.05
10
15
20
Time(sec)
25
30
35
40
Fig 4.14 a) Amplitude of vibration at top storey of 2D frame by placing TMD at top
storey when, corresponding to compatible time history as per spectra of IS-1894(Part1):2002 for 5
69
0.025
disp without TMD
disp with TMD
0.02
0.015
Displacement(m)
0.01
0.005
0
-0.005
-0.01
-0.015
-0.02
10
15
20
Time(sec)
25
30
35
Fig 4.14 b) Amplitude of vibration at top storey of 2D frame by placing TMD at top storey
when, El Centro(1940) earthquake loading acting on the structure.
Fig 4.14 Amplitude of vibration at top storey of 2D frame by placing TMD at top storey
when subjected to different earthquake loadings.
70
-4
x 10
-1
-2
-3
10
12
14
16
18
20
Fig 4.15 Amplitude of vibration at top storey of 2D frame by placing TMD at top storey
when subjected to sinusoidal acceleration
71
CHAPTER-5
SUMMARY AND FURTHER SCOPE OF WORK
5.1) Summary:
Current trends in construction industry demands taller and lighter structures, which
are also more flexible and having quite low damping value. This increases failure
possibilities and also, problems from serviceability point of view. Several techniques
are available today to minimize the vibration of the structure, out of which concept of
using of TMD is one. This study is made to study the effectiveness of using TMD for
controlling vibration of structure. A numerical algorithm was developed to model the
multi-storey multi-degree of freedom building frame structure as shear building with a
TMD. Another numerical algorithm is also developed to analyse 2D-MDOF frame
structure fitted with a TMD. A total of three loading conditions are applied at the base
of the structure. First one is a sinusoidal loading and the second one corresponding to
compatible time history as per spectra of IS-1894(Part -1):2002 for 5% damping at
rocky soil and the third one is 1940 El Centro Earthquake record (PGA = 0.313g).
and second being the 1940 El Centro Earthquake it has been found that increasing
the mass ratio of the TMD decreases the displacement response of the structure.
73
References
1) A. Baz (1998), Robust control of active constrained layer damping, Journal of Sound
and Vibration 211 pp467480.
2) A. Baz, (2000) Spectral nite element modelling of wave propagation in rods using
active constrained layer damping, Journal of Smart Materials and Structures9 pp372
377.
3) A. Chattopadhyay, Q. Liu, H. Gu, (2000) Vibration reduction in rotor blades using
active composite box beam, American Institute of Aeronautics and Astronautics
Journal 38 pp11251131.
4) Alexander Nicholas A, Schilder Frank(2009) Exploring the performance of a
nonlinear tuned mass damper Journal of Sound and Vibration 319 pp 445462
5) Alli H, Yakut O.(2005)Fuzzy sliding-mode control of structures. Engineering
Structures; 27(2)
6) Barkana I. (1987) Parallel feed forward and simplified adaptive control International
Journal of Adaptive Control and Signal Process;1(2):pp95-109.
7) Barkana I. (2005)Gain conditions and convergence of simple adaptive control
Internat J Adapt Control Signal Process;19(1):pp13-40.
8) Barkana I, Kaufman H.(1993)Simple adaptive control of large flexible space
structures. IEEE Trans Aerospace Electron System; 29(4).
9) Bitaraf Maryam, Ozbulut Osman E,Hurlebaus Stefan(2010) Application of semiactive control strategies for seismic protection of buildings with MR dampers
Engineering Structures
74
21) Dyke SJ, Spencer BF.(1996)Seismic response control using multiple MR dampers. In
2nd international workshop on structural control. Hong Kong University of Science
and Technology Research Centre.
22) Garg Devendra P, Anderson Gary L(2003) Structural vibration suppression via
active/passive techniques Journal of Sound and Vibration 262 pp 739-751
23) Ghosh A, Basu B(2004) Effect of soil interaction on the performance of tuned mass
dampers for seismic applications Journal of Sound and Vibration 274 pp 10791090
24) Guo Y.Q, Chen W.Q(2007) Dynamic analysis of space structures with multiple tuned
mass dampers Engineering Structures 29 ,pp33903403
25) Housner G. W,Bergman L. A, and Caughey T. K(1996) Structural control: past,
present, and future Journal of Engineering Mechanics, Vol.123, No.9,Paper No.
15617.
26) Huang W, Gould PL, Martinez R, Johnson GS.(2004)Non-linear analysis of a
collapsed reinforced concrete chimney. Earthquake Engineering Structural
Dynamics;33(4):pp485-98.
27) Hurlebaus S, Gaul L. (2006)Smart structure dynamics. Mechanical System Signal
Process; 20:pp255-81.
28) Inaudi, J. A. (1993). "Active isolation and innovative tuned mass dampers for vibration
reduction," PhD dissertation, University of California, Berkeley, California.
29) Inaudi J. A. (1997) Modulated homogeneous friction: a semi-active damping
strategy Earthquake Engineering Structural Dynamics; 26(3):pp361-76.
30) Inaudi, J. A., and De la Llera, J. C. (1992). "Dynamic analysis of nonlinear structures
using state-space formulation and partitioned integration schemes." Rep. No.
UCB/EERC-92//8, Earthquake Engineering Research Centre, University of California,
Berkeley, California.
76
31) Inaudi, J. A., and Kelly, J. M. (1992). "A friction mass damper for vibration control."
Rep. No. UCB/EERC-92//5, Earthquake Engineering Research Centre, University of
California, Berkeley, California.
32) Inaudi, J. A., and Kelly, J. M. (1993). "On the linearization of structures containing
linear-friction energy dissipating devices." Proc., Damping '93, San Francisco, Calif.
33) Jo Byung-Wan, Tae Ghi-Ho (2001) Structural vibration of tuned mass installed three
span steel box bridge International journal of pressure vessels and piping 78 pp
"667-675.
34) Johnson, J. G., Reaveley, L. D., and Pantelides, C. P. (2003). A rooftop tuned mass
damper frame. Earthquake Engineering Structural Dynamics,32(6),pp965984.
35) Jung HJ, Choi KM, Spencer BF, Lee IW.(2006) Application of some semi-active
control algorithms to a smart base-isolated building employing MR dampers.
Structural Control Health Monitoring 13:pp693-704.
36) K. Cunefare,(2000) State-switched absorber for vibration control of point-excited
beams, Proceedings of ASME International Mechanical Engineering Conference and
Exposition, Vol. 60, pp. 477484
37) K. Cunefare, S. De Rosa, N. Sadegh, (2001) G. Larson, State switched
absorber/damper for semi-active structural control, Journal of Intelligent Material
Systems and Structures 11 pp300310.
38) Kaynia, A.M., Veneziano, D. and Biggs, J.,(1981) "Seismic Effectiveness of
Tuned Mass Dampers", Journal of Structural Division Proceedings of ASCE,
(I07) T8, Paper no. 16427.
39) Kerber F, Hurlebaus S, Beadle BM, Stbener U(2007). Control concepts for an active
vibration isolation system. Mechanical System Signal Process21:pp3042-59.
77
40) Kitamura, H., Fujita, T, Teramoto, T, and Kihara, H. (1988). "Design and analysis of a
tower structure with a tuned mass damper." Proceedings of 9th World Conference on
Earthquake Engineering Vol. VII, Tokyo, Japan.
41) Kwok K.C.S(1995) Performance of tuned mass dampers under wind loads
Engineering Structures, Vol. 17, No. 9, pp. 655~67
42) Lee CC.(1995)Fuzzy logic in control system: fuzzy logic controller part I and part II.
IEEE Trans System Man Cybern;20:pp404-18.
43) Lee Chien-Liang, ChenYung-Tsang(2006) Optimal design theories and applications
of tuned mass dampers. Engineering Structures 28 pp 4353
44) Li, C. (2002). Optimum multiple tuned mass dampers for structures under the ground
acceleration based on DDMF and ADMF. Earthquake Engineering Structural
Dynamics,31(4),pp 897919.
45) Li, C. (2003). Multiple active-passive tuned mass dampers for structures under the
ground acceleration. Earthquake Engineering Structural Dynamics,32(6),pp949964.
46) Lin Chi-Chang, Lu Lyan-Ywan, Lin Ging-Long(2010) Vibration control of seismic
structures using semi-active friction multiple tuned mass dampers Engineering
Structures
47) Li Hua-Jun, Hu Sau-Lon James(2002) Tuned Mass Damper Design for Optimally
Minimizing Fatigue Damage Journal of Engineering Mechanics, Vol. 128, No. 6
48) Luft, R. W. (1979). Optimal tuned mass dampers for buildings. Journal of Structural
Division, 105(12), pp27662772.
49) McNamara, R. J. (1977) Tuned mass dampers for buildings. Journal of Structural
Division, 103(9), pp17851798.
78
Flows",
Journal of Wind
79
60) Sanchez E, Shibata T, Zadeh La.(1997)Genetic algorithms and fuzzy logic systems:
soft computing perspectives. River Edge (NJ): World Scientific Publishing.
61) Setareh, M., and Hanson, R. (1992). Tuned mass dampers to control floor vibration
from humans.". Structural Engineering., ASCE, 118(3),741-762.
62) Shamali Bijan, Al-Dawod Mohammed(2003) Performance of a ve-storey benchmark
model using an active tuned mass damper and a fuzzy controller. Engineering
Structures 25 pp 15971610
63) Shimazu T, Araki H(1996) Survey of actual effectiveness of mass damper systems
installed in buildings. Eleventh world conference on Earthquake Engineering, Paper
no.809
64) Singh, M. P., Singh, S., and Moreschi, L. M. (2002). Tuned mass dampers for
response control of torsional buildings. Earthquake Engineering and Structural
Dynamics,31(4), pp749769.
65) Sobel K, Kaufman H, Mabius L. (1982)Implicit adaptive control for a class of
MIMOsystems IEEE Trans Aerospace Electron System; AES-18(5).
66) Spencer BF, Dyke SJ, Sain MK, Carlson JD.(1997)Phenomenological model of a
magnetor-heological damper. Journal of Engineering Mechanics;123(3):pp230-8.
67) TakewakiI
(2000).Soil-structure
random
response
reduction
via
TMD-VD
70) Vickery, B.J. and Davenport, A.G.,( 1970), An Investigation of the Behaviour in
Wind of the Proposed Centrepoint Tower in Sydney, Australia, Engineering
Science Research. Dept., BLWT-70 , University of Western Ontario.
71) W. Liao, K. Wang, (1998) Characteristics of enhanced active constrained layer
damping treatments with edge elements, Part 1: Finite element model and
experimental validation, American Society of Mechanical Engineers Journal of
Vibration and Acoustics 120 886893.
72) Warburton, G. B. (1982). "Optimum absorber parameters for various combinations of
response and excitation parameters." Earthquake Engineering and Structural
Dynamics, Vol. 10,pp381-491.
73) Wardlaw, R.L. and Moss, G.F.,(1970) "A Standard Tall Building Model for the
Comparison of Simulated Natural Winds in Wind Tunnels", CAARC, CC-662
MTech 25.
74) Webster, A. c., and Vaicaitis, R. (1992). "Application of tuned mass dampers to
control vibrations of composite floor systems." Engineering. Journal, 29(3), pp116124.
75) Williams SR.( 2004)Fault tolerant design for smart damping systems. St. Louis
(MO): Department of Civil Engineering, Washington University.
76) Wong K.K.F(2008) Seismic Energy Dissipation of Inelastic Structures with Tuned
Mass Dampers Journal of Engineering Mechanics, Vol. 134, No. 2
77) Wong, K. K. F., and Yang, R. (1999). Inelastic dynamic response of structures using
force analogy method. Journal of Engineering Mechanics, 125(10),pp11901199.
78) Xu, K., and Igusa, T. (1992). Dynamic characteristics of multiple tuned mass
substructures with closely spaced frequencies. Earthquake Engineering and
Structural Dynamics,21(12), pp10591070.
81
82