RESPONSE CONTROL OF TALL BUILDINGS USING TUNED LIQUID DAMPERS

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1 11 Internatonal RASD Conference 20 th 1-3 July 2013 Psa 3 RESPONSE CONTROL OF TALL BUILDINGS USING TUNED LIQUID DAMPERS S. K. Bhattacharyya CSIR Central Bulng Research Insttute Roorkee, Ina E-mal: srman_bhattacharyya@yahoo.com Keywors: Tune lqu ampers, Flu-structure nteracton, Cvl engneerng. ABSTRACT The present tren of the creaton of tall bulngs an the usage of lght weght hgh strength materals, though have create economy, reucton n space requrement etc., structurally these have become susceptble to the lateral loang ue to wn or earthquake. Several attempts are mae to control the response of tall systems by ntroucng control mechansms n the form of actve, passve or hybr system. Usage of lqu storage tanks n tall bulng system n the form of a passve control evce proves effectve. Several works have been carre out n the past to unerstan the effcacy of such system, whch popularly s known as Tune lqu ampers. The present paper eals wth the evelopment of a numercal coe to emonstrate the effcacy of such tune lqu ampers conserng flu structure nteractons. 1. INTRODUCTION The present tren towars tall bulngs an the use of lghtweght, hgh strength materals often accompane by ncrease flexblty an a lack of suffcent nherent ampng, ncrease ther susceptblty to exctatons such as ue to wn, ocean waves or earthquakes. To reuce the rsk of structural falures partcularly urng a catastrophc event t has become mportant to search for practcal an effectve evces for suppresson of the vbratons generate ue to such exctatons. Ths has necesstate explorng mechansms to suppress the vbratons of such tall bulngs by some sutable evces. The evces use for mtgatng structural vbraton may be categorze accorng to ther energy consumpton as Passve, Actve an Sem-actve or Hybr control systems. Several attempts n the past have been mae to evolve sutable types of structural control evces an erve ther effcaces. These nclue works of Housner et al. (1997), Spencer Jr. an San (1997), Soong an Spencer Jr. (2002) an Spencer Jr. an Nagarajaah (2003), amongst others. Passve control evces are systems whch o not requre external energy supply. Such systems are relable snce they are unaffecte by power outages, whch are common urng natural calamtes. Example of such system nclues base solaton (usng elastomerc an lea rubber bearngs), energy sspaton evces such as metallc ampers, vscous ampers, frcton ampers, tune mass ampers, tune lqu ampers etc. (Soong an Dargush (1997) an Kasa et al. (1998)). Actve control systems on the other han nvolves conserable amount of external power to operate actuators that supply a control force to the structure. The control force s generate epenng on the feeback of the structural response. They are more effectve than passve evces because of ther ablty to aapt to fferent loang contons an to control fferent moes of

2 vbraton. Examples of such systems nclue actve mass ampers (AMDs), actve bracng systems, etc. (Housner et al. (1994) an Sakamoto et al. (1994)). Sem-actve systems are vewe as controllable evces, wth energy requrements less than typcal actve control systems snce external power s only use to change evce s propertes such as ampng or stffness, an not to generate a control force. These functon as passve evces n case of power falure. Examples of such systems nclue varable orfce ampers, electro-rheologcal ampers, magneto-rheologcal flu amper, sem-actve varable stffness tune mass amper (SAIVS-TMD) etc. (Symans an Constantnou (1999)). Hybr control system utlzes the useful characterstcs of both systems whch mples the combne use of passve an actve systems or passve an sem-actve systems. The most common combnatons are hybr mass ampers (HMD), whch combne tune mass ampers wth actve actuators. Dampng s efne as the ablty of the structure to sspate a porton of the energy release urng a ynamc loang event an thus one of the most mportant parameters that lmt the response of the structures. Attachment of lqu tanks to the structure ntrouces capablty of nucng ampng n the system. The sloshng moton of the lqu that results from the vbraton of the structure sspates a porton of the energy release by the ynamc loang an therefore ncreases the equvalent ampng of the structure. These tank evces are referre to as Tune Sloshng Dampers (TSD) or smply Tune Lqu Dampers (TLD). The TLD system reles on the sloshng wave evelopng at the free surface of the lqu to sspate a porton of the ynamc energy. The growng nterest n lqu ampers s ue to ther low captal an mantenance cost an ther ease of nstallaton nto exstng an new structures. Thus TLD concept represents an excellent technque for up-grang the sesmc resstance of both exstng an new structures. The performance of TLD reles manly on the sloshng of lqu at resonance to absorb an sspate vbraton energy of the structure. Fuj et al (1990) carre out the full scale measurement of wn nuce vbratons of two actual tall structures- Nagasak Arport Tower (heght 42 m) an Yokohama Marne Tower (heght 101m). The splacements were reuce to about 40% upon nstallaton of Tune Sloshng Damper. Dynamc force frequency response functon of TLD was also expermentally etermne to stuy the effect of the TLD n whch the natural frequency of the water nse the contaner was tune to that of the structure. Ahsan Kareem (1990) stue the mtgaton of wn nuce moton of bulngs utlzng tune sloshng ampers. It was emonstrate by the authors that a sloshng amper can effectvely reuce the moton of bulngs when the funamental sloshng an bulng frequences are synchronze. Sun an Fujno [1] propose a sem analytcal moel for TLD usng a rg rectangular tank flle base on shallow water wave theory. The response of a SDOF structure ftte wth a TLD s expermentally stue an t s foun that TLD works satsfactorly for suppressng structural vbratons. Koh et al [2] nvestgate the use of lqu ampers whch are tune to fferent vbraton frequences of a mult-egree-of-freeom structure. It was observe by the authors that the poston of the lqu amper has a sgnfcant effect on the vbraton response. Takash Nomura [3] employe Arbtrary Lagrangan-Euleran (ALE) formulaton to hanle the free surface moton of the lqu n TLD. Nonlnear nteracton of lqu moton an structure moton was capture by the propose computatonal metho for the vortex-excte oscllaton of a crcular cylner as well as a TLD-structure nteracton problem. Tamura et al [4] carre out the fullscale measurements of the wn-nuce responses of bulngs to prove the effcency of tune lqu ampers (TLDs). The wn-nuce responses of the bulngs were measure before an after the nstallaton of TLDs. Vbraton perceve by occupants ue to aly wn was sgnfcantly reuce. The TLD coul reuce the acceleraton responses urng strong wns own to 1/2-1/3 of the response wthout the TLD, thus the habtablty an servceablty of bulngs were conserably mprove. Ikea an Nakagawa [5] analytcally an expermentally stue the non lnear sloshng amper n a rectangular tank. The water tank s attache to a structure to suppress the horzontal vbratons of the structure cause by a snusoal exctaton. Quanttatvely goo agreement was obtane between the theoretcal

3 characterstcs an the expermental results. Warntcha an Pnkaew (1997) propose a new mathematcal moel of lqu sloshng n rectangular tanks, whch nclues the effects of flow-ampenng evces. Ths moel can accurately represent the complex behavour of lqu sloshng an, at the same tme, s smple enough to be use n engneerng calculatons, an more mportantly, the effects of flow-ampenng evces can be analytcally evaluate. Ree et al (1999) numercally moelle the TLD as an equvalent tune mass amper wth non-lnear stffness an ampng. These are etermne such that the energy sspaton prove by the Non-lnear Stffness an Dampng (NSD) s equvalent to that of the TLD. Ths NSD moel captures the behavour of the TLD system uner a varety of loang contons. Thus NSD moel presente here s an equvalent TMD representaton of the TLD. An algorthm for upatng the NSD ampng an the stffness coeffcents n a tme hstory analyss of a SDOF structural system has been prove. Kanok-Nukulcha an Tam [6] propose a Lagrangan splacement-base flu element to moel large ampltue free surface moton of nearly ncompressble vscous flus n a tank of rectangular cross-secton uner ynamc exctaton for tune lqu amper applcatons. The penalty metho s employe to enforce the nearly ncompressble characterstc of flus. The effectveness of the propose moel was verfe by expermental results from the lterature. The results show that the propose non-lnear flu element can prect non-lnear behavors of large ampltue sloshng ue to ynamc exctaton, especally at near-resonant regon. Yamamoto an Kawahara (1999) presente a numercal stuy for structural control usng a tune TLD, whch conssts of sol tank flle wth lqu. The authors emonstrate that the compute results are closer to the expermental ones. Banerj et al (2000) carre out the stuy of the ynamc behavor of SDOF structure, rgly supportng a rg rectangular TLD tank wth shallow water. An attempt was mae to efne approprate esgn parameters of the TLD that s effectve n controllng the earthquake response of a structure through parametrc stues. Tat et al [7] formulate both lnear an nonlnear numercal moel of a TLD wth slat screens. The nonlnear moel of a TLD equppe wth ampng screens (Kaneko an Ishkawa, 1999) s presente. The nonlnear sloshng response s postulate usng shallow water theory (Lepelleter an Rachlen, 1988). A proceure to calculate the theoretcal value of the force coeffcent of a slat-type screen s presente an verfe from expermental results an s applcable for both wn (small exctaton) an earthquake (large exctaton) loang. The nonlnear moel s capable of moellng a TLD equppe wth multple screens at varous screen locatons nse the tank. The nonlnear moel s also verfe over a range of practcal flu epth to tank length rato values. An expermental program s conucte to assess the applcablty of the theoretcally etermne loss coeffcent by a TLD urng ynamc exctaton. Fransen [8] evelope a fully nonlnear 2-D -transforme fnte fference solver base on nvsc flow equatons n rectangular tanks. The flu moton s escrbe by nonlnear potental flow equatons allowng steep non overturnng waves to be capture. Twomensonal solutons are obtane usng a fnte-fference tme-steppng scheme on aaptvely mappe grs. The solver also removes the nee for free-surface smoothng. The flu moel s couple to an elastc support structure. The effectveness of the TLD s scusse through precton of couplng frequences an response of the tank-structural system for fferent tank szes, mass rato between flu an structure an tunng rato. Bhattacharyya et al [9] formulate a mxe Euleran Lagrangan fnte element moel to compute the nonlnear sloshng ampltue of lqu n lqu flle rectangular an crcular cylnrcal contaners subjecte to snusoal base exctaton. The soluton s obtane by the Galerkn metho. The fourth-orer Runge-Kutta metho s employe to avance the soluton n the tme oman. A regrng technque s apple to the free surface of the lqu, whch elmnates the numercal nstabltes wthout the use of artfcal smoothenng. Ths fnte element metho s use for computng the non-lnear sloshng response of lqu n a two mensonal rg rectangular tank wth baffles an crcular cylnrcal contaner wth annular baffle. Valty of the present moel s checke by comparng avalable results for the tank

4 wthout baffle. The effects of baffle parameters such as poston, menson, an numbers on the non-lnear sloshng response are also examne. The lqu tank attache to the structure, unergoes sloshng moton that results from the vbraton of the structure, sspates a porton of the energy release by the ynamc loang an therefore ncreases the equvalent ampng of the structure. In the present paper, ynamc characterstcs of an ealse bulng structure are stue when attache wth tune lqu flle tank as passve amper uner ynamc exctaton. The two systems, lqu system an the structural system n Fg.1 are stue n uncouple form. The couplng between the two systems s acheve n an teratve manner. Structure Flu 2. THEORETICAL FORMULATION Fgure 1. Structure an Flu System A rg contaner of wth L contanng ncompressble an nvsc lqu subjecte to horzontal oscllaton s consere. The statonary lqu heght s h an η represents the free surface sloshng elevaton. Flu oman Ω s boune by the free surface S 1 an flu-sol bounary nterface. Sol bounary conssts of tank wall an tank bottom as shown n Fg.2. Statonary free surface y Free surface uner sloshng h S 1 Ω x,t x L Fgure 2. Lqu sloshng n rg rectangular tank

5 2.1 Governng Equaton Conserng the lqu as nvsc & ncompressble, & flow rrotatonal, governng equaton may be wrtten by Laplace equaton n Ω as: 2 0 (1) where, ϕ(x,y,t) s the velocty potental. However, n a movng tank the total velocty potental ϕ may be splt nto two parts, potental functon ϕ t ue to tank moton & sturbe potental functon ϕ s ue to flu moton (2) For the tank movng n horzontal recton n vertcal plane, ϕ t may be expresse as Expressng Laplace equaton n terms of ϕ s t s t x xst (3) 0 (4) 2 s 2.2 Bounary Contons In a rg contaner soluton of Laplace equaton must satsfy the bounary conton s 0 on n where n s the unt normal vector rawn outwarly to the sol bounary s x s 0 ; 0 on S y xl/2 yh In Euleran form Knematc & Dynamc Bounary contons on free lqu surface are s s y t x x 2 on S 1 Knematc B.C s 1 s s g x xst 0 on S 1 Dynamc B.C t 2 In Lagrangan form equatons may be wrtten as x s y s ; Knematc B.C t x t y (5) (6) (7) (8) (9) s 1 s s s 2 g x xst Dynamc B.C t 2 y t (10)

6 3. FINITE ELEMENT FORMULATION y x,t x h S 1 Ω 3.1 Intal Impulse Conton Fgure 3. Fnte element moel of lqu sloshng Intally the flow starts wth a small horzontal tank velocty. Callng ths as an ntal mpulse conton, base on lnear theory where st 0 0 ; 0 & x x t s t st on free surface (11) x x 0 ; 0 on free surface (12) s x s ntal small tank velocty. st For fnte element analyss entre flu oman s scretze usng four noe quarlateral elements. As scusse earler to start wth, ntal conton may be taken as x x 0 ; 0 on free surface (13) s st Wth the known velocty potental at free surface noes Laplace equaton s solve to obtan unknown noal velocty an pressure satsfyng the bounary contons. 4. FINITE ELEMENT SOLUTION OF LAPLACE EQUATION Spatal scretzaton of Laplace equaton s one by means of Galerkn weghte resual technque. ϕ s s approxmate as Applyng Galerkn s prncple N (14) s s n x L y 2 2 N s s x y (15) Assumng n s the total number of noal ponts of the scretze lqu oman an n be the number of noes corresponng to the free surface bounary, the unknown noal values s gven by n-n, also equal to the number of equatons resultng from Galerkn s approxmaton, represente as n\n.

7 Applyng approprate bounary conton an known velocty potental ϕ at free surface noes, the resultng equaton becomes N s N N x y N N x y s j j j j n jn \ n jn K f where s the vector of unknown noal values. n \ n (16) (17) K j N N N N x y (18) x jn \ n x y jn \ n y j j f N N N N x y (19) n \ n j j j x jn x y jn y 5. FLUID-STRUCTURE INTERACTION MODEL The two systems, flu system an the structural system are stue n uncouple form. The two systems are terate n the sense that flu system wll experence the floor response an n turn flu system wll exert hyroynamc sloshng force on the structure. The equaton of moton of the structure beng solve for a flu-structure nteracton problem s: [ M] { u } [ C] { u } [ K] { u } F F (20) st st st e Where, M s mass matrx of the structure, C s ampng matrx of the structure, K s the stffness matrx, u st s noal splacement vector. F s the exctaton vector, e for earthquake exctaton: F -[ M] { l} x ; e l s the nfluence vector of the structure subject to groun exctaton. F s the total hyroynamc sloshng force ue to sloshng n tanks, N F { m} F ; 1 F s the hyroynamc sloshng force ue to sloshng of TLD at th floor, N s the number of lqu amper nstalle over the storeys, m s the nfluence vector for the lqu amper stuate at th floor. x s groun acceleraton. g Stffness matrx K an consstent mass matrx M for the gven mult-egree freeom structure s etermne. Dampng matrx C of the structure s erve from Raylegh ampng whch consers mass an stffness-proportonal ampng for the case of classcal ampng. Natural frequences an the natural moe shapes of vbraton s obtane by performng the free vbraton analyss of the structural system. g

8 Incorporatng the ampng term n Dynamc bounary conton s 1 s s s 2 g x xst. s t 2 y t s the ampng coeffcent n the ampng term s, whch prmarly takes nto account the ampng effect ue to sloshng of the lqu. x s the base acceleraton nuce n the tank ue to structure response whch s same as st the floor acceleraton, to whch the TLD s rgly connecte to. Thus, T { }.{ st} m u. 6. CALCULATION OF HYDRODYNAMIC SLOSHING FORCE (21) x st can be obtane as Hyroynamc sloshng force s obtane by ntegratng the hyroynamc pressure over the tank projecte area, whch n turn acts on the on the structure as base shear force. 1 2 F b p( L / 2, y, t) y p( L / 2, y, t) y h h (22) Where 1 an 2 are the free surface sloshng elevaton at the two se walls of the tank, an p(l/2,y,t) an p(-l/2,y,t) are the lqu pressures at x= ±L/2. b s breath of tank, the menson n other orthogonal recton. The convergence n the soluton s acheve by teratve proceure both for structural splacement an the pressure n the lqu. Parametrc stues are carre out to observe the effect of slosh ampng n the response of the structural system. The parameters stue are the tunng rato, rato of sloshng frequency to moal frequency of structure, mass rato, rato of mass of amper to structure, water epth rato, rato of statonery lqu heght to length of the tank etc. A few typcal results are ncate heren to emonstrate the effcacy of tune lqu amper n controllng the response of the structural system. Fg.4 shows the splacement of the top floor of the structural system for a mass rato of 0.8. Fgure 4. Response of structural system wth an wthout Tune lqu amper Fg.5 shows the response of the structural system wth an wthout the presence of lqu amper for a water epth rato of 1.0.

9 Fgure 5. Response of structural system wth an wthout Tune lqu amper The evelope numercal coe s frst valate aganst the avalable results n lterature an subsequently the effects of fferent parameters on the effcacy of tune lqu amper are stue. As shown n the fgures, the result emonstrates the effectveness of the tune lqu ampers. SELECTED REFERENCES [1] Sun LM, Fujno Y - A sem analytcal moel for tune lqu amper (TLD) wth wave breakng - Journal of Flus an Structures 1994; 8: [2] Koh C G, Mahatma S, Wang C M - Reucton of structural vbratons by multple-moe lqu ampers - Engneerng Structures 1995; 17(2): [3] Nomura T. - ALE fnte element computatons of flu-structure nteracton problems Computer - Methos n Apple Mechancs an Engneerng 1994; 112: [4] Tamura Y, Fuj K, Ohtsuk T, Wakahara T, Kohsaka R - Effectveness of tune lqu ampers uner wn exctaton - Engneerng structures 1995; 17(9): [5] Ikea T, Nakagawa N - Non-lnear vbratons of a structure cause by water sloshng n a rectangular tank - Journal of Soun an Vbraton 1997; 201(1): [6] Kanok-Nukulcha W, Tam B T - Structure-flu nteracton moel of tune lqu ampers - Internatonal Journal For Numercal Methos In Engneerng 1999; 46: [7] Tat M J, Damatty A A, Isyumov - An nvestgaton of tune lqu ampers equppe wth ampng screens uner 2D exctaton - Earthquake Engneerng an structural Dynamcs 2005; 34: [8] Fransen J B. - Numercal prectons of tune lqu tank structural systems - Journal of Flus an Structures 2005; 20: [9] Bswal K C, Bhattacharyya S K, Snha P K. - Non-lnear sloshng n partally lqu flle contaners wth baffles - Internatonal Journal of Numercal Methos n Engneerng, 2006; 68, [10] Chen W, Haroun MA, Lu F. - Large ampltue lqu sloshng n sesmcally excte tanks. - Earthquake Engneerng an Structural Dynamcs 1996; 25: [11] Faltnsen OM, Rognebakke OF, Tmokha AN. Classfcaton of three-mensonal nonlnear sloshng n a square-base tank wth fnte epth. Journal of Flus an Structures 2005; 20:81 103

10 [12] Lamb H. Hyroynamcs, Cambrge Unversty Press: Lonon, 1932; [13] Naln Kumar Srvastava Response control of Hghrse Structures usng Tune Lqu Dampers M.Tech thess, I.I.T. Kharagpur. [14] Okamoto T, Kawahara M - Two-mensonal sloshng analyss by Lagrangan fnte element metho - Internatonal Journal for Numercal Methos n Flus 1990; 11: [15] Wakahara T, Ohyama T, Fuj K. Suppresson of wn-nuce vbraton of a tall bulng usng tune lqu amper. Journal of Wn Engneerng an Inustral Aeroynamcs 1992; 41-44: