Research Paper

Tuned Sloshing Damper in Response Control of Tall Building StructureS K BHATTACHARYYAProfessor, Department of Civil Engineering, IIT Kharagpur, India

(Received on 16 April 2016; Accepted on 02 May 2016)

The paucity of space and requirements of building infrastructure has driven us to explore for taller building systems. Alsoa large number of construction materials has emerged and are being used extensively in buildings. The usage of light weighthigh strength materials reduces the space requirement and also becomes economical. However, such structures havestructurally become susceptible to the lateral loading generated due to wind or earthquake. Attempts are made to control theresponse of tall building systems by introducing control mechanisms in the form of active, passive or hybrid system. Usageof liquid storage tanks in tall building system in the form of a passive control device proves effective. Several works havebeen carried out in the past to understand the efficacy of such system, which popularly is known as tuned liquid dampersor tuned sloshing dampers (TSD). The present paper deals with the development of a numerical code to demonstrate theefficacy of such tuned sloshing damper considering fluid structure interaction effect.

Keywords: Sloshing; Damper; Response Control; Building, Passive System; Tuned Sloshing Damper (TSD)

*Author for Correspondence: E-mail: srimankb@gmail.com

Proc Indian Natn Sci Acad 82 No. 2 June Spl Issue 2016 pp. 223-231Printed in India. DOI: 10.16943/ptinsa/2016/48415

Introduction

The paucity of space and the present trend towardstall buildings, the use of lightweight, high strengthmaterials often accompanied by increased flexibilityand a lack of sufficient inherent damping, increasetheir susceptibility to excitations such as due to wind,ocean waves or earthquakes. To reduce the risk ofstructural failures particularly during a catastrophicevent it has become important to search for practicaland effective devices for suppression of the vibrationsgenerated due to such excitations. This hasnecessitated exploring mechanisms to suppress thevibrations of such tall buildings by some suitabledevices. The devices used for mitigating structuralvibration may be categorized according to their energyconsumption as Passive, Active and Semi-active orHybrid control systems. Several attemptsin the pasthave been made to evolve suitable types of structuralcontrol devices and derive their efficacies. Theseinclude works of Housner et al., 1997; Spencer Jr.and Sain, 1997; Soong and Spencer Jr., 2002 andSpencer Jr. and Nagarajaiah, 2003, amongstothers.Passive control devices are systems which do

not require external energy supply. Such systemsare reliable since they are unaffected by poweroutages, which are common during natural calamities.Example of such system includes base isolation (usingelastomeric and lead rubber bearings), energydissipation devices such as metallic dampers, viscousdampers, friction dampers, tuned mass dampers, tunedliquid dampers etc. (Soong and Dargush, 1997; Kasaiet al., 1998). Active control systems on the other handinvolves considerable amount of external power tooperate actuators that supply a control force to thestructure. The control force is generated dependingon the feedback of the structural response. Theseare more effective than passive devices because oftheir ability to adapt to different loading conditionsand to control different modes of vibration. Examplesof such systems include active mass dampers(AMDs), active bracing systems, etc. (Housner etal., 1994; Sakamoto et al., 1994).

Semi-active systems are viewed as controllabledevices, with energy requirements less than typicalactive control systems since external power is onlyused to change device’s properties such as damping

Published Online on 29 June 2016

224 S K Bhattacharyya

or stiffness, and not to generate a control force. Thesefunction as passive devices in case of power failure.Examples of such systems include variable orificedampers, electro-rheological dampers, magneto-rheological fluid damper, semi-active variable stiffnesstuned mass damper (SAIVS-TMD) etc. (Symans andConstantinou, 1999). Hybrid control system utilizesthe useful characteristics of both systems whichimplies the combined use of passive and activesystems or passive and semi-active systems. The mostcommon combinations are hybrid mass dampers(HMD), which combine tuned mass dampers withactive actuators.

Damping is defined as the ability of the structureto dissipate a portion of the energy released during adynamic loading event and thus one of the mostimportant parameters that limit the response of thestructures. Attachment of liquid tanks to the structureintroduces capability of inducing damping in thesystem. The sloshing motion of the liquid that resultsfrom the vibration of the structure dissipates a portionof the energy release by the dynamic loading andtherefore increases the equivalent damping of thestructure. These tank devices are referred to as TunedSloshing Dampers (TSD). In general sloshing of liquidcauses problem in tank devices, however, in this casethe sloshing of liquid in tank is used to its advantage.The TSD system relies on the sloshing wavedeveloping at the free surface of the liquid to dissipatea portion of the dynamic energy. The growing interestin liquid dampers is due to their low capital andmaintenance cost and their ease of installation intoexisting and new structures. Thus TSD conceptrepresents an excellent technique for up-grading theseismic resistance of both existing and newstructures.The performance of TSD relies mainly onthe sloshing of liquid at resonance to absorb anddissipate vibration energy of the structure. The fullscale measurement of wind induced vibrations of twoactual tall structures - Nagasaki Airport Tower (height42 m) and Yokohama Marine Tower (height 101m)were carried out (Fuji et al., 1990). The displacementswere reduced to about 40% upon installation of TunedSloshing Damper. Dynamic force frequency responsefunction of TSD was also experimentally determinedto study the effect of the TSD in which the naturalfrequency of the water inside the container was tunedto that of the structure. The mitigation of wind inducedmotion of buildings utilizing tuned sloshing dampers

was studied (Ahsan Kareem, 1990). It wasdemonstrated by the authors that a sloshing dampercan effectively reduce the motion of buildings whenthe fundamental sloshing and building frequencies aresynchronized. A semi analytical model for TSD usinga rigid rectangular tank filled based on shallow waterwave theory was proposed (Sun and Fujino, 1992).The response of a SDOF structure fitted with a TSDwas experimentally studied and it was found that TSDworks satisfactorily for suppressing structuralvibrations investigated The use of liquid damperswhich are tuned to different vibration frequencies ofa multi-degree-of-freedom structure was studied (Kohet al., 1994). It was observed by the authors that theposition of the liquid damper has a significant effecton the vibration response. Takashi Nomura, 1994employed Arbitrary Lagrangian-Eulerian (ALE)formulation to deal with the free surface motion ofthe liquid in TSD. Nonlinear interaction of liquid motionand structure motion was captured by the proposedcomputational method for the vortex-excited oscillationof a circular cylinder as well as a TSD-structureinteraction problem. The full-scale measurements ofthe wind-induced responses of buildings to prove theefficiency of tuned liquid dampers (TLDs) was carriedout (Tamura et al., 1995). The wind-inducedresponses of the buildings were measured before andafter the installation of TLDs. Vibration perceivedby occupants due to daily wind was significantlyreduced. The TLD could reduce the accelerationresponses during strong winds down to 1/2-1/3 of theresponse without the TLD, thus the habitability andserviceability of buildings were considerablyimproved. Ikeda and Nakagawa, 1997 studied the non-linear sloshing damper in a rectangular tank bothanalytically and experimentally. The water tank isattached to a structure to suppress the horizontalvibrations of the structure caused by a sinusoidalexcitation. Quantitatively good agreement wasobtained between the theoretical characteristics andthe experimental results. Warnitchai and Pinkaew,1997 proposed a new mathematical model of liquidsloshing in rectangular tanks, which include the effectsof flow-dampening devices. This model canaccurately represent the complex behaviour of liquidsloshing and, at the same time, is simple enough to beused in engineering calculations, and more importantly,the effects of flow-dampening devices can beanalytically evaluated. Reed et al., 1999 numerically

Tuned Sloshing Damper in Response Control of Tall Building Structure 225

modelled the TLD as an equivalent tuned massdamper with non-linear stiffness and damping. Theseare determined such that the energy dissipationprovided by the Non-linear Stiffness and Damping(NSD) is equivalent to that of the TLD. This NSDmodel captures the behaviour of the TLD systemunder a variety of loading conditions. Thus NSD modelpresented here is an equivalent TMD representationof the TLD. An algorithm for updating the NSDdamping and the stiffness coefficients in a time historyanalysis of a SDOF structural system has beenprovided. Kanok-Nukulchaiand Tam, 1999 proposeda Lagrangian displacement-based fluid element tomodel large amplitude free surface motion of nearlyincompressible viscous fluids in a tank of rectangularcross-section under dynamic excitation for tuned liquiddamper applications. The penalty method is employedto enforce the nearly incompressible characteristicof fluids. The effectiveness of the proposed modelwas verified by experimental results from theliterature. The results show that the proposed non-linear fluid element can predict non-linear behaviorsof large amplitude sloshing due to dynamic excitation,especially at near-resonant region.Yamamoto andKawahara, 1999 presented a numerical study forstructural control using a tuned TLD, which consistsof solid tank filled with liquid. The authorsdemonstrated that the computed results are closer tothe experimental ones. Banerji et al. (2000) carriedout the study of the dynamic behavior of SDOFstructure, rigidly supporting a rectangular TLD tankwith shallow water. An attempt was made to defineappropriate design parameters of the TLD that iseffective in controlling the earthquake response of astructure through parametric studies. B. Nanda, 2010had carried out a work on the application of tunedliquid damper for controlling structural vibration ofbuildings. The author made an exhaustive study andhad demonstrated the efficacy of the tuned sloshingdampers. J Mondal, 2014 had carried out anexperiment in the laboratory to demonstrate that theliquid sloshing helps in reducing structural vibration offramed structures. N K Rai et al., 2013 had attemptedto reduce the response of existing buildings by carryingout retrofitting using tuned liquid dampers. The authorshad demonstrated that liquid sloshing in tanks can helpreducing the vibrational response of structures evenwhen retrofitted in existing buildings. Tait et al. (2005)formulated both linear and non-linear numerical model

of a TLD with slat screens. The nonlinear model of aTLD equipped with damping screens (Kaneko andIshikawa, 1999) is presented. The non-linear sloshingresponse is postulated using shallow water theory(Lepelletier and Raichlen, 1988). A procedure tocalculate the theoretical value of the force coefficientof a slat-type screen is presented and verified fromexperimental results and is applicable for both wind(small excitation) and earthquake (large excitation)loading.The non-linear model is capable of modellinga TLD equipped with multiple screens at variousscreen locations inside the tank. The non-linear modelis also verified over a range of practical fluid depth totank length ratio values. An experimental program isconducted to assess the applicability of thetheoretically determined loss coefficient by a TLDduring dynamic excitation. Frandsen, 2005 developeda fully non-linear 2-D -transformed finite differencesolver based on inviscid flow equations in rectangulartanks. The fluid motion is described by non-linearpotential flow equations allowing steep non overturningwaves to be captured. Two-dimensional solutions areobtained using a finite-difference time-steppingscheme on adaptively mapped grids. The solver alsoremoves the need for free-surface smoothing. Thefluid model is coupled to an elastic support structure.The effectiveness of the TLD is discussed throughprediction of coupling frequencies and response ofthe tank-structural system for different tank sizes,mass ratio between fluid and structure and tuning ratio.Bhattacharyya et al., 2006 had formulated a mixedEulerian-Lagrangian finite element model to computethe non-linear sloshing amplitude of liquid in liquid filledrectangular and circular cylindrical containerssubjected to sinusoidal base excitation. The solutionis obtained by the Galerkin method. The fourth-orderRunge-Kutta method is employed to advance thesolution in the time domain. A re-gridding technique isapplied to the free surface of the liquid, whicheliminates the numerical instabilities without the useof artificial smoothening. This finite element methodis used for computing the non-linear sloshing responseof liquid in a two dimensional rigid rectangular tankwith baffles and circular cylindrical container withannular baffle. Validity of the present model is checkedby comparing available results for the tank withoutbaffle. The effects of baffle parameters such asposition, dimension, and numbers on the non-linearsloshing response are also examined.

226 S K Bhattacharyya

Tuned Sloshing Dampers can be broadlyclassified into two categories, shallow-water and deep-water dampers based on the ratio of the water depthto the tank length in the direction of motion. The TSDsystem relies on the sloshing wave developing at thefree surface of the fluid to dissipate a portion of thedynamic energy. The growing interest in liquiddampers is due to their low capital and maintenancecost and their ease of installation into existing andnew structures. Thus TSD concept represents anexcellent technique for up-grading the seismicresistance of both existing and new structures.

The liquid tank attached to the structure,undergoes sloshing motion that results from thevibration of the structure, dissipates a portion of theenergy released by the dynamic loading and thereforeincreases the equivalent damping of the structure.

In the present paper, dynamic characteristics ofan idealised building structure in 2-D form are studiedwhen attached with tuned liquid filled tank as passivedamper under dynamic excitation. The two systems,liquid system and the structural system in Fig. 1 arestudied in uncoupled form. The coupling between thetwo systems is achieved through iterations.

considered. The stationary liquid height is h and represents the free surface sloshing elevation. Fluiddomain is bounded by the free surface S1 and fluid-solid boundary interface S2. Solid boundary consistsof tank wall and tank bottom as shown in Fig. 2.

Theoretical Formulation

A rigid container of width L containing incompressibleand inviscid liquid subjected to horizontal oscillation is

Fig. 1: Structure and fluid system

Governing Equation

Considering the liquid as inviscid and incompressible,and flow irrotational, governing equation may bewritten by Laplace equation in as:

2 0 (1)

where,(x, y, t) is the velocity potential. However, ina moving tank the total velocity potential may besplit into two parts, potential functiont due to tankmotion and disturbed potential functions due to fluidmotion.

t s (2)

For the tank moving in horizontal direction invertical plane, t may be expressed as

t stx x (3)

Expressing Laplace equation in terms of s

2 0s (4)

Boundary Conditions

In a rigid container, solution of Laplace equation mustsatisfy the boundary condition

20 on Ss

n

(5)

Fig. 2: Liquid sloshing in rigid tank

Tuned Sloshing Damper in Response Control of Tall Building Structure 227

where n is the unit normal vector drawn outwardly tothe solid boundary

2/ 2

0 ; 0 on Ss s

x L y hx y

(6)

In Eulerian form Kinematic and DynamicBoundary conditions on free liquid surface are

1 on S

Kinematic B.C

s s

y t x x

(7)

1

10 on S

2Dynamic B.C

ss s stg x x

t

(8)

In Lagrangian form, equations may be writtenas

; Kinematic B.Cs sdx dy

dt x dt y

(9)

12

2

Dynamic B.C

s ss s st

dg x x

dt y t

(10)

Finite Element Formulation

Initial Impulse Condition

Initially the flow starts with a small horizontal tankvelocity. Calling this as an initial impulse condition,based on linear theory

0 ; 0

&t s t st

on free surface

x x

(11)

0 ; 0s stx x

on free surface

(12)

where (0)stx is initial small tank velocity..

For finite element analysis entire fluid domain isdiscretized using four noded quadrilateral elements.

As discussed earlier to start with, initial conditionmay be taken as

0 ; 0s stx x

on free surface

(13)

With the known velocity potential at free surfacenodes Laplace equation is solved to obtain unknownnodal velocity and pressure satisfying the boundaryconditions.

Finite Element Solution of Laplace Equation

Spatial discretization of Laplace equation is done bymeans of Galerkin weighted residual technique.

s is approximated as

s s i ii n

N

(14)

Applying Galerkin’sprinciple

2 2

2 2 0s siN dx dy

x y

(15)

Assuming n is the total number of nodal pointsof the discretized liquid domain and nd be the numberof nodes corresponding to the free surface boundary,the unknown nodal values is given by n–nd, also equalto the number of equations resulting from Galerkin’sapproximation.

Applying appropriate boundary condition andknown velocity potential d at free surface nodes,

Fig. 3: Finite element model of liquid sloshing

228 S K Bhattacharyya

the resulting equation becomes

\

( \ )

d

d

si i j j

j n n

i j d j dj n

N ds N N dx dyn

N N dx dy i n n

(16)

where is the vector of unknown

nodal nalues

K f

(17)

\ \d d

j ji iij

j n n j n n

N NN NK dx dy

x x y y

(18)

d d

j ji idj

j n j n

N NN Ndx dy

x x y y

(19)

F-S Interaction Model

The two systems, fluid system and the structuralsystem are studied in decoupled form. The twosystems are iterated in the sense that fluid systemwill experience the floor response and in turn fluidsystem will exert hydrodynamic sloshing force on thestructure.

The equation of motion of the structure beingsolved for a fluid-structure interaction problem is:

[ ] { } [ ] { } [ ]{ }st st st e dM u C u K u F F (20)

Where, M is mass matrix of the structure, C isdamping matrix of the structure, K is the stiffnessmatrix, ust is nodal displacement vector.

Fe is the excitation force vector, for earthquake

excitation; Fe = –[M]{l} gx l is the influence vector of

the structure subjected to ground excitation. Fd is thetotal hydrodynamic sloshing force due to sloshing in

tanks,1

{ }dN

i idi

F m F

Fi is the hydrodynamic sloshing force due to

sloshing of TSD at ith floor, Nd is the number of liquiddamper installed over the storeys, mi is the influencevector for the liquid damper situated at ith floor.

gx is ground acceleration.

Stiffness matrix K and consistent mass matrixM for the given multi-degree freedom structure isdetermined. Damping matrix C of the structure isderived from Rayleigh damping which considersmass and stiffness-proportional damping for the caseof classical damping.

Natural frequencies and the natural modeshapes of vibration are obtained by performing thefree vibration analysis of the structural system.

Incorporating the damping term in Dynamicboundary condition

12

2

.

ss ss

st s

dy t

dtg x x

(21)

is the damping coefficient in the damping term.s,which primarily takes into account the dampingeffect due to sloshing of the liquid.

stx is the base acceleration induced in the tank

due to structure response which is same as the flooracceleration, to which the TSD is rigidly connected

to. Thus stx can be obtained as T{ } .{ }stm u .

Calculation of Sloshing Force

Hydrodynamic sloshing force is obtained byintegrating the hydrodynamic pressure over the tankprojected area, which in turn acts on the structure asbase shear force.

1

2

( / 2, , )

( / 2, , )

h

h

p L y t dy

F b

p L y t dy

(22)

Where 1 and 2 are the free surface sloshingelevation at the two side walls of the tank, and p(L/

Tuned Sloshing Damper in Response Control of Tall Building Structure 229

2,y,t) and p(–L/2,y, t) are the liquid pressures at x =±L/2. b is breadth of tank, the dimension in otherorthogonal direction. The convergence in the solutionis achieved by an iterative procedure both forstructural displacement and the pressure developedin the liquid.

Parametric studies are carried out to observethe effect of slosh damping in the response of thestructural system. The parameters studied are thetuning ratio, ratio of sloshing frequency to modalfrequency of structure, mass ratio, ratio of mass ofdamper to structure, water depth ratio, ratio ofstationery liquid height to length of the tank etc. Afive storeyed building with overhead water tank asTSD is considered for the parametric investigations.Properties of the beams and columns are uniformthroughout the storeys. First modal frequency for theconsidered structure is 6.2 rad/sec. TSD will be usedto suppress the first vibration mode of this buildingsubjected to ground excitation. Tuning the fundamentalsloshing of the overhead water tank (as TSD) to thefirst modal frequency of the building gives the lengthof the tank as 0.8 m in the direction of the excitation.Fig. 4 shows the details of the building considered forparametric studies.

For the parametric investigation to determinethe optimal TSD parameters the building is subjectedto harmonic ground excitation.

20

0where 0.007 ; 6.2 / sec

. . sin( . );g e e

em and rad

u x t

x

Thus the three frequencies namely structuremodal frequency, sloshing frequency and the excitationfrequency are kept synchronized

Fig. 5(A) shows the displacement of the top floorof the building for a mass ratio of 1.5. Fig. 5(B) showsthe displacement of the structure and the sloshingdisplacement. The phase difference of the twodisplacements is quite distinct.

In the present model, water depth ratio (h/L) iskept in the range of 1-2. Parametric investigations

Fig. 4: Test Structure for the parametric investigation

Fig. 5: Response of structural system with and without TunedSloshing damper. Column height = 4m, beam length= 8 m, damping ratio = 5%, EI beam = 17.5e-4 kNm2, EIcolumn = 27.9e-4 kNm2, Beam crossectional area =0.12m2, Column crossectional area = 0.24m2, UDL onbeam = 40 kN/m

A

B

230 S K Bhattacharyya

have been carried out to analyse the performance ofTSD with the varying water depth ratios. For thevarying water depth ratios inherent damping in thestructure is kept 5% and the mass ratio as 2% keepingthe water tank at the top floor (i.e. 5th floor). Table 1indicates the percentage reduction in the displacementof the top floor for different water-depth ratio, withthe following parameters: Structure Damping = 5%;Tuning Ratio = 1; Mass Ratio = 2%; Top FloorDisplacement without TLD = 0.09 m.

A parametric study was undertaken to study theeffect of mass proportioning on the displacement ofthe building structure. Accordingly the mass wasdistributed between two floors instead of lumping atone floor. Table 2 indicates the percentage reductionin floor displacement due to the mass distribution intwo floors.

Concluding Remarks

Maximum percentage reduction in the response ofthe structure as top floor displacement was obtainedfor water depth ratio equal to 1. Increasing the waterdepth ratio from 1 to 2 caused the gradual decline inthe effectiveness of the overhead water tank asdamper, but still water depth of 2 provided a significantamount of percentage reduction in the top floordisplacement as 42.1%. This implied that the water

depth ratio in the range of approximately 1.0-1.5 mayprovide appreciable amount of mitigation up to 44%.

Investigations carried out for the varying massproportion showed that TSD maintained itsperformance quite effectively even after proportioningthe damper mass as 100-0, 90-10, 80-20, 70-30, and60-40 % over the top two storeys. In the present caseof five storey structure under harmonic groundexcitation maximum percentage reduction of 47.7%in the response of the structure as top floordisplacement was observed for mass proportioningof 90% at 5th floor and 10% at 4th floor. It was alsoobserved that tuned water tank performs effectivelyas a damper even for the mass proportioning of 60%at 5th floor and 40% at 4th floor providing a percentagereduction of 44.4 in the structure top floordisplacement.

Significant performance of deep-water TSDwith varying mass proportion implied that if enoughtop floor space is not available for the installation ofTSD one can carry out the proportioning of thedamper mass in the upper storeys for multi-storeyedbuildings. Also from the structure design point of viewinstead of lumping the mass at the top storeyproportioning of damper mass in the upper storeyswill reduce the increase in the stresses in the structuralmembers due to the addition of the damper mass.

Table 1: Performance of TSD against varying water depth

Water depth ratio (h/L) 0.8 1.0 1.25 1.50 1.75 2.0

Mesh size 12x12 12x12 14x12 16x12 18x12 20x12

Top floor displacement (m) 0.0477 0.0475 0.0488 0.0502 0.0512 0.0521

Percentage reduction 47 47.2 45.7 44.2 43.1 42.1

Table 2: Performance of TSD against varying mass ratio

Mass Proportions % 5th =100% 5th =90% 5th =80% 5th =70% 5th =60%4th =0 % 4th =10 % 4th =20 % 4th =30 % 4th =40 %

Top Floor Displacement (m) 0.0475 0.0471 0.0481 0.0491 0.05

Percentage Reduction 47.2 47.7 46.6 45.4 44.4

Other parameters assumed in the study are: Structure Damping = 5%; Mass Ratio = 2%; Tuning Ratio = 1; Water Depth Ratio = 1; TopFloor Displacement without TSD = 0.09 m

Tuned Sloshing Damper in Response Control of Tall Building Structure 231

References

Biswal K C, Bhattacharyya S K and Sinha P K (2006) Non-linear

sloshing in partially liquid filled containers with baffles

International Journal of Numerical Methods in Engineering

68 317-337

Chen W, Haroun M A and Liu F (1996) Large amplitude liquid

sloshing in seismically excited tanks Earthquake

Engineering and Structural Dynamics 25 653-669

Faltinsen O M, Rognebakke O F and Timokha A N (2005)

Classification of three-dimensional nonlinear sloshing in a

square-base tank with finite depth Journal of Fluids and

Structures 20 81-103

Frandsen J B (2005) Numerical predictions of tuned liquid tank

structural systems Journal of Fluids and Structures 20

309-329

Ikeda T and Nakagawa N (1997) Non-linear vibrations of a

structure caused by water sloshing in a rectangular tank

Journal of Sound and Vibration 201 23-41

J Mondal et al., (2014) Tuned liquid damper – Proceedings of 3rd

International Conference on Mechanical Engineering and

Mechatronics, August 14-15, paper 68

Kanok-Nukulchai W and Tam B T (1999) Structure-fluid

interaction model of tuned liquid dampers International

Journal for Numerical Methods in Engineering 46 1541-

1558

Koh C G, Mahatma S and Wang C M (1995) - Reduction of

structural vibrations by multiple-mode liquid dampers

Engineering Structures 17 122-128

Lamb H (1932) Hydrodynamics Cambridge University Press:

London 619-621

N K Rai et al. (2013) Tuned liquid sloshing water damper: A

robust device for seismic retrofitting International journal

of Environmental science: Development and Monitoring

4

Nanda B (2010) Application of tuned liquid damper for controlling

structural vibration M. Tech thesis submitted at NIT

Rourkela

Nomura T (1994) ALE finite element computations of fluid-

structure interaction problems Computer Methods in

Applied Mechanics and Engineering 112 291-308

Okamoto T and Kawahara M (1990) Two-dimensional sloshing

analysis by Lagrangian finite element method International

Journal for Numerical Methods in Fluids 11 453-477

Srivastava Nalin (2007) Response control of tall buildings using

tuned liquid dampers – M. Tech thesis submitted to IIT

Kharagpur

Sun L M and Fujino Y (1994) A semi analytical model for tuned

liquid damper (TLD) with wave breaking Journal of Fluids

and Structures 8 471-488

Tait M J, Damatty A A and Isyumov (2005) An investigation of

tuned liquid dampers equipped with damping screens under

2D excitation Earthquake Engineering and structural

Dynamics 34 719-735

Tamura Y et al. (1995) Effectiveness of tuned liquid dampers

under wind excitation -Engineering structures 17 609-621

Wakahara T, Ohyama T and Fujii K (1992) Suppression of wind-

induced vibration of a tall building using tuned liquid damper

Journal of Wind Engineering and Industrial Aerodynamics

41-44 1895-1906.