[2](1990)Reduction of Wind Induced Motion Utilizing a Tuned Sloshing Damper

8/3/2019 [2](1990)Reduction of Wind Induced Motion Utilizing a Tuned Sloshing Damper

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Journal of Wind Engineering and Industrial Aerodynamics,36 (1990) 725-737 725Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

Reduc t ion o f Wind Induced Mot ion Ut i l iz ing a Tuned Sloshing DamperAhsan Kareem*

A B S T R A C TServicea bi l i ty of bui ld ings is affe c ted by excess ive accelera t ion exper ie nced a t thetop f loors in wind s torms that ma y cause d iscomfort to the occupants. To en sure funct ionalpe r fo rmance o f t a l l bu i ldings i t i s impor tan t to keep the f requency o f ob jec t ionab le mo t ionlevels below the d iscom fort threshold . This paper addresses a new approach that faci li ta tesmit igat ion of wind indu ced motion of bui ld ings u t i l iz ing tuned s loshing dampers . Firs t , atheo re t ica l background o f the f lu id s lo sh ing sys tem i s g iven , wh ich i s fo l lowed bymo deling of s loshing f lu id and s tructura l sys tems. An exam ple of a ta l l bui ld ing equippedwith a tuned s loshing d am per is presented to i llus tra te the effec t ivene ss of such d evices inmi t iga t ing s t ruc tu ra l mo t ion . F ina l ly , a b r ie f d i scuss ion o f the po ten tia l fo r p rac tica lapplications is presented.

I N T R O D U C T I O NTh e current t rend of bui ld ings w ith ever increas ing heights and l ights facades hasled to the construct ion of re la t ively f lexib le s t ructures possess ing qui te low damping. Theresu l t ing sens i t iv i ty o f these bu i ld ings to dynamic exc i ta t ion by wind has inc reased .Bes ides va r ious fa i lu re poss ib i l it i e s, c ladd ing and pa r t i t ion damage , se rv iceab i l i ty o f abui ld ing is an importan t des ign cr i ter ia . Th e serv iceabi l i ty of a bui ld ing is affec ted byexcess ive acce le ra t ion expe r ienced a t the top f loo rs in wind s to rms tha t may cause

d iscomfor t to the bu i ld ing occupan ts . The re fo re , to ensu re func t iona l pe r fo rmance o f t a l lbu i ld ings i t is im por tan t to keep the f requency o f ob jec t ionab le mo t ion leve l s be low thedisc om fort threshold . Variou s poss ib i l i t ies exis t to achieve th is goal , the g lobal des ignmod if ica t ions presente d in Table 1 range from consider ing a l ternat ive s tructural sys tems toae rodyn amic m od i f ica t ion . Fu r the r de ta i ls on the e f fec t iveness o f each a l te rna t ive a rediscussed in Ka reem (1983).T h e u s e o f t u n e d m a s s d a m p e r s a n d v i s c o e l a s t ic d a m p e r s i s g a i n i n g w i d eacceptan ce in bui ld ing industry as evidence d by recent implem enta t ion of these devices inta i l bui ld ings and o the r f lex ib le s t ructures (e.g ., M cNam ara , 1977, W iesner , 1986, Keel ,1987 and Kitam ura, et al. 1988). Re cen t studies hav e dem onstra ted that sloshing fluid in aconta in er i f proper ly tuned acts l ike a tuned m ass dam per in reducing s tructura l response(Sun & Karee m, 1986; Kare em & Sun, 1987; M odi & Welt , 1987; Fuj ino , e t a l ., 1988;

Tam ura e t a l. , 1988) . Ear l ier s tudies , though not par t icular ly focusse d on their applica t ionto engineer in g s tructures , a lso conclud ed that for a proper se lec t ion of des ign parameters ,c o n t a i n e r s p a r t i a l l y f i l l e d w i t h f l u i d s s e r v e a s g o o d v i b r a t i o n d a m p e r s ( Sa y a r &Bau mg arten , 1982) . Dam pers u t i l iz ing l iquid motions have been u t i l ized successfu l ly insa te ll i te s and on ocean vesse l s (Bhu ta & K o v ~ , 1966 , Har ri s & Crede , 1987) . Mos t o f* Profe ssor and Director, Structural Aerodynamics and Ocean System Modeling Laboratory, University ofHous ton, Houston, TX 77204-4791.

0167-6105/90/$03.50 1990---Elsevier Science Publishers B.V.


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t hese inves t iga t ions cons idered s impl i f i ed mo del ing of the pr imary and the secon darysystems. Kareem & Sun (1987) reported stochastic response of structures (Multi-degree-of- f reed om sys tems) wi th fluid-containing appendages (also m ode led as mul t iple-degree-of - f r eedom sys tem) . A bui ld ing wi th a water t ank s i tua ted a t any f loor , exci t ed by anearthquake, was used to i llust rate the method ology. An im por tant feature of the com binedsys tem is tha t the r esponse o f the pr imary sy s tem i s suppres sed when one of the s loshingmod es of the secondary flu id appendage i s tuned to the fundamen ta l mod e of the pr imarysys tem. In the fo l lowin g sec tion a br i ef d i scuss ion concerning the behavior of thecom bined sys tem is presented.

Tuned Sloshing Dampers (TSD) can be broadly c l as s i f i ed in to two ca tegor i es ,shal low-water and deep-water dampers . Thi s c l as s i f ica t ion i s based on the r a t io of thewater surface elevat ion in the direct ion of mot ion to the water depth. Like a T M D, the TSDwh en installed in a structural sy stem indirec tly imparts additional da m ping to the sy stem bymo difying the f requenc y response funct ion of the s t ructure, thereby redu cing the response.In the shal low water ease the T SD damp ing or ig inates primar i ly f rom en ergy d i s s ipa t ionthrough the ac t ion of the in t ernal f lu id v i scous forces and f rom wa ve breaking . Theprovi s ion of the sur face contaminat ion , such as PVC beads or a l i p a long the wal lparameter can ad d to the d i s s ipa t ion of s loshing energy. Fo r the deep-water damper , inaddi t ion to v i scous damp ing, the presence o f baf f les or s creens m ay fur ther increase thedamping. The dam ping mechan i sm is , therefore , dependent on the am pl i tude of the f lu idmo t ion and wave-brea king pat terns . To c orrect ly mo del the contr ibut ion of a TSD to thedyn am ical behavior of the combine d sys tem, the t ransfer funct ion of the TSD mu st accountfor the resultant c han ges in dam ping values for different mo tion amplitudes and directions.

The m ot ion of l iquids in r igid containers has been a subject of ma ny s tudies in thepas t f ew decades , due to i t s f r equent appl i ca t ion in severa l engineer ing d i sc ip l ines .Al thou gh the ph enom enon o f l iquid s loshing in spherical and cyl indr ical shaped containershas been exten s ively s tudied, l iquid s loshing in pr isma t ic rectangu lar tanks has rec eivedl imited attent ion. A large nu mb er of the present and previous s tudies ha ve been bas ed onl inear and/or nonl inear potent ial f low theo ry (e.g. , Lam b, 1947; Cooper , 1960; Abramson ,1966; Cok ele t , 1977; and Ho lyer , 197 9) . Unfor tunate ly , due to the under ly ing potent ia lf low assumptions , these s tudies c anno t take into acco unt the ef fect of f luid viscos i ty whichi s centr a l to the TSD concept . Ches ter (1968) and Verhagen an d Wi jngaarden (1978)ut i li z ing a per turbat ion approach so lved the shal low-water wave eq uat ion , but v i scouseffects were neglected. M ore recent ly, Fal t inson (1978) int roduced a f icti t ious term in theEuler equat ions to ar t i f icially include the ef fect of viscous diss ipation. Ho wev er , the formof th i s damp ing t erm c aused cons iderable nu mer ica l d i f f i cu l ty in the so lu t ion of theequations of mot ion.

The subjec t of v i scous d i s s ipa t ion in progres s ive w aves has been addres sed in anum ber of c las s i ca l papers ( e .g . , Bouss inesq , 1868; Ho ugh , 1897; and Lam b, 1945) .More r ecent ly , Keulegan (1959) inves tiga ted the deca y m odulus o f f in i te -ampl i tude wavesin a rectang ular bas in. In this analys is , i t was a ssum ed that the ene rgy diss ipat ion wasent i r e ly due to the bou ndary l ayer s near the bas in wal l s. Un der cer ta in condi t ions , abou nda ry laye r type solution provided satisfactory ag reem ent with the experimental studies.Prosperett i (1976) investigated the transient behavior o f small-amplitude stand ing wave s onthe plane surface of an infinitely deep viscous l iquid. Th e results exh ibited som e departurefrom the e xis t ing s tudies for al l but smal l values o f viscos ity. Th e hy drody nam ic aspects o fthe mo tion of a viscous flu id havin g a free surface in a rolling tank has been investigated byDe mirbi lek (1983) u t i lizing both s im pl i f ied analyt ical me thods an d num erical techniques .M odi et al . (1988) inv es t igated energy diss ipat ion due to a s loshing l iquid in toms shapeddampers both analy t i ca lly and exper imenta l ly , t he ir analys i s account s for both nonl inear


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727an d v i sco u s e f fec t s . M o re recen t l y , Lep e l l e t i o r an d Ra i ch l en (1 9 8 8 ) rep o r t ed a n o n l in ea r ,d i sp e rs iv e , d is s i p a t i v e mo d e l t o d esc r i b e t h e f l u id mo t io n i n a rec t an g u l a r b as in ex c i t ed b yan o sc i l l a t o ry , t r an s i en t , u n id i rec t io n a l t r an s l a t i o n a l mo t io n . I t wa s n o t ed t h a t fo r ac o n t i n u o u s l y e x c i t e d b a s i n a n d f o r s h a l l o w w a t e r w a v e s t h e l i n e a r t h e o r y b e c o m e si n a d e qu a t e n e a r re s o n a n c e. T h e i r m o d e l s h o w e d a g o o d a g r e e m e n t w i th t h e e x p e r im e n t sfor a l l cases invest iga ted .M O D E L I N G O F S L O S H I N G F L U ID A N D S T R U C T U R A L S Y S TE M S

Th e f l u id s lo sh in g sy s t em can b e rep re sen t ed b y an eq u iv a l en t mech an i ca l m o d e l i nwh ich t h e f l u id i s r ep l aced b y l u mp ed f l u id masses , sp r i n g s an d d ash p o t s [F ig . I ] . Th em e c h a n i c a l c h a r a c t e r i s t i c s o f t h e e q u i v a l e n t s y s t e m a r e e s t a b l i s h e d b y f o l l o w i n g t h edyna m ic s imi l i tude of the s losh ing f lu id (po ten t ia l f low theory) or by experim enta l methods(Ab ra mso n , 1 96 6 ). Th e en e rg y t ran s fe r red t o t h e f lu id may b e d i s s i p a t ed b y t h e v isco u sac t i o n o f t h e f lu id , d amp in g d ev i ces o r t h e wav e b reak in g ac t i o n . A t h eo re ti ca l e s tima t io no f t h e d amp in g av a i l ab l e i n s l o sh in g may i n c lu d e co n s id e ra t i o n o f t h e n o n l i n ea r wav esu r face p ro f i l e an d t h e co mp u ta t i o n o f t h e en e rg y d i s s i p a t ed i n a v i sco u s f l u id [Lamb ,1 9 45 ]. A f i n i t e -e lemen t m o d e l i s b e in g d ev e lo p ed t o i n v es t ig a t e th e d y n am ics o f a li q u ids lo sh in g i n a p a r t i a l l y - f i l led r i g id t an k , i n c lu d in g t h e e f fec t s o f f ree -su r face n o n l i n ea r i ty ,v i sco s i t y an d en e rg y d i s s ip a t io n , an d t o v a l i d a t e th e n u m er i ca l r esu l ts b y m ean s o f a se r ie so f co n t ro l led l ab o ra to ry ex p e r imen t s . Th e l i q u id s l o sh in g m o d e l i s b ased o n t h e n o n l i n ea rshal low -w ater w ave theory in two horizonta l d i rec t ions .

T h e m e c h a n i c a l p a r a m e t e r s o f a ty p i c a l T S D b a s e d o n p o t e n ti a l f lo w t h e o r y f o rr e c t a n g u l a r ta n k s a r e s u m m a r i z e d he r e . T h e e q u i v a l e n t s l o s h i n g m a s s m ~ w h e r e= 1 , - - - J i s g ive n by

nag = {8 tanh [28- 1)~r] /~3r(28- 1)} ML (1 )

in wh ich r = h / a , h = d ep th o f f l u id , a = l en g th o f t an k i n t h e d i rec t i o n o f mo t io n an dM L = to ta l f lu id ma ss , m e i s equal to the f lu id m ass w hich osc i l la tes w i th the s t ruc ture in ar i g id b o d y mo d e an d i s eq u a l t o ME - ~ m an d k = m co2 for g = 1 ,2 , ----J .~.=1 8 8 ~:

T h e p r i m a r y s t r uc t u ra l s y s t e m m a y b e c o n v e n i e n t l y m o d e l e d b y a l u m p e d m a s ssy s t em co n s i s ti n g o f n - l u mp ed m asses . Th e co m b in ed s l o sh in g f l u id an d s t ruc tu ra l sy s t emc a n b e r e p r e s e n t e d b y t h e m o d e l s h o w n i n F i g. 2 . T h e e q u a t i o n s o f m o t i o n f o r t h eco m b in ed p r imary an d seco n d a ry sy s t ems a reM s ~ s + C s x s + K s x s = f ( t ) (2 )

i n wh ich


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728 [ : I x }s = ; x s = - .X

I n t h e p r e c e d i n g e q u a t i o n X a n d x a r e d i s p l a c e m e n t s c o r r e s p o n d i n g t o t h e s tr u c t u r a l a n ds l o s h i n g fl u i d d e g r e e s o f f r ~ . , d o m -X = [X l , X 2 . . . . XN] T ; x = [Xl, x 2 . . . . x j] T . (3 )

T h e s u b m a w i c e s i n t h e s y s t e m m a s s a n d s t i ff n e ss m a t r i c e s a r e g i v e n b y

I 1 M 2 1M = j( M N + M ~ - ~ n m )m=lm = E x 12

m j

K =

m

K I + K 2 - K 2- K 2 K 2 + K 3

(I~ +J

~ K m )m = l

k_a

i u

0 . . . . . . k l0 - - -k2v

0 . . . . . . k j xN


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[ 1 1 12 0k_ = (4)k jT h e d a m p i n g s u b m a t r i c e s f o l l o w th e f o r m o f s ti f fn e s s m a t r i c es . T h e c o m b i n e d s y s t e mrep resen t s N + J deg rees o f f reedom. The a ssoc i a t ed f requency and the mod e shapes o f thecom bined sys t em a re ob t a ined f rom the fo l lowing equa tionsS S S[_K .S _ M C0 i ]~ ) i = 0 (5 )

Alternat ively , a perturbat ion app roach m ay be u t i l ized which perm i ts the evaluat iono f t h e e i g e n p r o p e r t ie s o f t he c o m b i n e d s y s t e m i n t e r m s o f t he d y n a m i c p r o p e r ti e s o f t h es t ruc tu ra l (p r imary ) and s lo sh ing f lu id ( seconda ry ) sy s t em [K areem & Sun , 1987 ]. Th i sfo rmu la t i on he lp s t o avo id compu ta t i on d i f f i cu l t i e s i n t he numer i ca l so lu t i on o f t hee igenva lues t ha t may a r i se a s a re su l t o f t he d i f fe rence i n t he magn i tudes o f va r iouse l emen t s in t he mass and t he s t i ffness ma t r i ces . The re sponse o f t he combin ed sys t em toae rody nam ic l oad ing ma y be eva lua t ed emp loy ing a moda l supe rpos i t ion techn ique . I t i sa l so impor t an t t o no t e t ha t i n gene ra l, t he combined sy s t ems a re no t moda l ly dampe d eveni f i t i s a s sume d tha t each o f the two subsys t em s a re p ropo r t i ona l ly dam ped . Fo r spec i a lc a s e s , o n e m a y i n v o k e t h e a s s u m p t i o n o f c l a s s i c a l d a m p i n g f o r t h e c o m b i n e d s y s t e mwi thou t i n t roduc ing a s izeab l e e r ro r . Ho we ver , fo r nonc l a ss i ca l l y dam ped sys t em s , t hee q u a t i o n s o f m o t i o n m a y b e e x p r e s s e d i n t e r m s o f a s t a t e - v e c t o r w h i c h p r o v i d e s aconve n ien t so lu t ion [e .g ., Me i rov i t ch , 1980 and Karee m, 1987 ]. The re spo nse s t a ti s ti c sm ay a l so be ob t a ined , w i thou t re so r ti ng t o the no rm a l mod e app roach , by u t i l iz ing d i rec tf requency dom ain app roach i nvo lv ing sys t em t rans fe r func tion [K areem, 1987 ].

The p reced ing ana ly s i s can be s imp l i f i ed i f t he con t r i bu t ion o f s t ruc tu ra l h ighe rm odes can be ignored . Al though s tudies ha ve shown that for the wind induced accelera t ionresponse t he h ighe r m odes do hav e s i zeab le con t r ibu t ion [Kareem , 1981 ]. In t h is ca se t hes t ruc tu ra l sy s t em i s rep resen t ed by a m ode-gen e ra l i zed sy s t em wi th re spec t t o t he funda -men ta l m ode [F ig .3 ] . The t rans fe r func t ion o f t he com bined sys t em i s g iven byHx(iC0) = 1 (6)

J( i - ( C O ) 2 + i 2 ~ b ( C O ) ) - ( ~ - - - ) 2 Z ~A_mn

O)b COb C O b n = l " ' b

I + i 2 ; n( ~ - -- )C O n( I - ( ~ _ ) 2 + i 2 ~ n ( 0 ) ) )

C O n C O ni n wh ich t he sym bo l s have been de f ined in F ig . 3 . As no t ed ea r l ie r , con t ra ry t o a typ i ca lT M D ( t u n ed m a s s d a m p e r ) t h e p a r a m e t e r s , in p a r ti c u la r , t h e d a m p i n g a v a i l a b l e in t h es lo sh ing f l u id i s a func tion o f w ave su r face t opo logy and wa ve b reak ing wh ich depends onthe amp l i t ude o f mo t ion o f the TSD con ta ine r . As s t a t ed ea r l i e r t ha t t he e s t ima t ion o fdam ping can be bes t mad e by expe r im en ta l me thod . In l igh t o f t h is t he t rans fe r func t ion o fthe s lo sh ing f l u id i n a TSD con ta ine r can be de t e rmined b y exc i t ing t he TSD wi th a known


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b ase acce l e ra t i o n o n a sh ak e t ab l e o r a s imi l a r fac i li t y an d measu r in g t h e fo rce b e tween t h eco n t a in e r an d t h e sh ak e tab l e . By mean s o f a d u m m y co n t a in e r wi th o u t an y f l u id , th ein e r ti a fo rce in t ro d u ced b y t h e co n ta in e r mass can b e su b s t ract ed . No rm a l i z in g th e fo rced u e t o t h e s l o sh in g f l u id b y t h e i n p u t fo rce g iv en b y t h e f l u id mass an d t h e sh ak e t ab l eaccelera t ion , a convenien t t ransfer funct ion can be es tab l ished . Equat ion 6 can be recast inthis case to the fo l lowing fo rm

1Hx(ifo) = j (7)

fOb COb n = l M b

in which Ha(it0) i s the t rans fer funct ion o f the s losh ing system .T h e n u m b e r o f s l o s h i n g d a m p e r m o d e s t o b e i n c o r p o r a t e d i n t h e a n a l y s i s i sg e n e r a l ly s m a l l a n d f o r m a x i m u m e f f e c t i v en e s s th e f u n d a m e n t a l s l os h in g m o d e i s t u n e dwi th t h e fu n d am en ta l mo d e o f t h e b u i l d in g . In th i s ca se t h e n a tu ra l f req u en cy o f th efu n d a me n ta l s l o sh in g m o d e i s v e ry c lo se t o t h e f ftr st n a tu ra l f req u en cy o f t h e b u i ld in g .Fu r th e rmo re , fo r sma l l d i sp l acemen t o f t h e b u i l d in g t o p , t h e TS D t ran s fe r fu n c t io n i s l i k e lyto b e v e ry c lo se to t h a t o f TM D. Ho we v er , a t la rg e r to p f l o o r d i sp l acemen t , t h e s l o sh in gsy s t em w i l l h av e h ig h e r d am p in g w h ich a l t e r s th e t ran s fe r fu n c t io n ch a rac t e r i s t ic s o f th es lo sh in g f l u id . Th i s i s e s sen t i a l l y a sma l l r ed u c t i o n i n t h e n a tu ra l f req u en cy an d anassocia ted decrease in the ampl i tude of the transfer function . This m ay in tu rn in f luence theo p t im a l tu n in g o f t h e co mb in ed sy s t em w h ich i n ad d it i o n t o o th e r p a rame te rs d ep en d s o nthe dam ping con t r ibu ted by the s losh ing f luid .

E X A M P L EA b u i ld in g 1 0 0 ft sq u a re i n p l an , an d 6 0 0 f t ta l l was m o d e l ed a s a f i v e d eg ree -o f -f reed o m sy s t em . Th e sa l i en t ch a rac t e r i s ti c s o f th e b u il d in g a re p re sen t ed i n Tab l e I I. As lo sh in g d am p er w as a t t ach ed t o t h e to p l ev e l an d t h e fu n d amen ta l p e r i o d o f s l o sh in g w astuned to the f trs t na tura l per iod of the ta l l bu i ld ing . Th e conta iner d imens ions in p lan were2 0 f t x 2 0 f t an d w a t e r h e ig h t eq u a l t o 2 .0 6 f t. Th e b u i l d in g re sp o n se t o t h e a lo n g win dl o a d in g w i t h a n d w i t h o u t th e T S D w a s c o m p u t e d . T h e a l o n g w i n d l o a d in g w a s m o d e l e dfo l l o win g a co v a r i an ce sy n th es is sch eme b y i n v o k in g s t ri p an d q u as i - s t ead y t h eo r i e s [e. g. ,Ka reem , 19 8 5] . De t a i l s m ay b e fo u n d i n Ka reem [19 8 5] . Th e mo d e-g en e ra l i zed l o ad swere ev a lu a t ed b ased o n t h e m o d e sh ap es co mp u ted fo r each co n f ig u ra t io n .In F ig . 4 , th e t ran s fe r fu n c ti o n o f a t y p i ca l b u i l d in g - TS D sy s t em i s p lo tt ed . Th eest im ated dam ping fo r liqu id s losh ing i s taken to be equal to 4 percent . I t i s no ted tha t theaddi t ion o f the TS D sign i f ican t ly modi f ies the t ransfer funct ion which thereby fac i l i ta tes the

red u c t i o n o f b u i l d in g re sp o n se . Th e m o d i f i ca t i o n in t h e tran s fe r fu n c t i o n re su l ti n g f ro mdifferen t mas ses s losh ing l iqu id i s dem onst ra ted in Fig . 5. I t i s obv ious tha t an increase inthe l iqu id mass ra t io to the bu i ld ing m ass in the f t rs t m ode resu l t s in a conc om itan t decreasein t h e t ran s fe r fu n c t io n am p l i tu d e a s we l l a s t h e l o ca ti o n o f t h e p eak s . An o p t ima l v a lu e o ft h e mass ra t i o can b e d e r i v ed t o max imize th e b en e f it s d er i v ed an d t o min imize p rem iu m fo rthe addi tional mass . The bu i ld ing accelera t ion response and the bu i ld ing - TS D accelera t ionrespo nse are g iven in Fig . 6 . Th e resu l ts demo nst ra te the effec t ivene ss of the dam per.


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PRACTICALAPPLICATIONSTh e i n i ti a l su ccess o f t h e co n cep t a s ap p l i ed t o win d sen s i t i v e s t ru c tu re s h as b eendem onst ra te d in pre l im inary s tud ies carr ied ou t in the U.S. an d Japan .Th e an a ly s i s sh o w n in t h is p ap e r d emo n s t ra t e s t h e e f fec t i v en ess o f t u n ed s l o sh in gd am p ers i n red u c in g t h e s t ru c tu ra l r e sp o n se . Th ese d am p ers u n l ik e o th e r p ass iv e d amp e rssu ch a s TM Ds req u i re m in im u m m a in t en an ce an d an ex i s t in g w a t e r s to rag e fac i l it y i n t heb u i l d in g ma y b e u t i li zed t o h e lp mi t i g a te mo t io n o f t a ll b u il d in g s. Th e co n v en i en ce o fins ta l la t ion off ers g rea t po ten t ia l fo r incorpora t ion in ex is t ing s t ruc tures and for tem pora ryu se d u r in g co n s t ru c t i o n p h ase , e sp ec i a l l y co n t ro l l in g t h e mo t io n o f e l ev a to r sh a f ts . Th ep ro sp e c t s fo r th e i r ap p l ica t i o n in o f f sh o re p l a tfo rm s a re a l so p ro m is in g . Th e p o t en t i a lb en e f i t s a r is i n g f ro m th e ap p l i ca t i o n o f th e TS D co n cep t t o o f f sh o re p la t fo rms ran g e f ro mr e d u c i n g t h e m o t i o n s o f t e n s io n l e g p l a t f o r m s a n d t h e v i b r a t i o n o f t h e ir t e t h er s , t oi m p r o v i n g t h e f a t i g u e l i f e o f j a c k e t - t y p e p l a t f o r m s a n d r e d u c i n g t h e s t r e s s e s in t h eprodu ct ion r i sers and f lare bo om s of bo th ex is t ing and new s tructures.Recen t l y a p o r t ab l e v e rs io n o f t u n ed s l o sh in g d am p ers h as b een i n s ta l led i n a i rp o r t

t o wers i n Jap an t o red u ce win d i n d u ced m o t io n o f th ese f l ex ib le s t ru c tu re s . Th e se rv i ce -ab i l i ty o f su ch s t ru c tu re s t o en su re c o m fo r t o f a i rp o r t t r a ff i c co n t ro ll e r s i s an im p o r t an ti ssue [T am ura e t al ., 1988] . M ul t ip le layers o f l iqu id in c i rcu lar conta iners w ere u t i l ized inth is ap p l i ca t i o n an d fu l l - sca le re sp o n se m easu rem en t s sh o w ed a red u c t i o n i n t h e re sp o n selevel o f these towers . Othe r po ten t ia l appl ica t ions ex is t fo r f lex ib le br idge s t ruc tures , ch im -neys and com m unicat ion towers . M ore analy t ica l and experim enta l s tud ies are needed to beab l e t o b e t t e r mo d e l t h e f req u en cy re sp o n se fu n c t io n o f TSD s fo r a wid e ran g e o f s t ru c tu ra lre sp o n se , e s p ec i a l l y in t h e ca se o f b u i ld in g s w h ich ex p e r i en ce co mb in ed l a t e ra l - to r s i o n a lmo t io n . In t h e ca se o f t o r s i o n a l mo t io n , d amp ers l o ca t ed n ea r t he o u t e r wa l l s o f th e t o pf lo o r wo u ld p ro v id e an o p t ima l sp ac in g.

C O N C L U S I O N SI t i s d e m o n s t r a t e d t h a t a s l o s h in g d a m p e r c a n e f f e c t i v e l y r e d u c e t h e m o t i o n o fbui ld ings when the fundam enta l s losh ing and bui ld ing frequencies are synchron ized . Lik ea t u n ed mass d am p er , t h e t u n ed s l o sh in g d amp e r imp ar t s in d i rec tl y ad d i ti o n a l d am p in g t othe syste m by mo di fy in g the frequenc y respon se funct ion of the s t ruc ture; thereby reducingresp o n se . Th e s l o sh in g f l u id sy s t em ab so rb s s t ru c tu ra l v ib ra ti o n en e rg y an d d i s s i p a t e s b ym ean s o f v isco u s ac t i o n o f t h e f l u id , wav e b reak in g o r d amp in g d ev i ces . Th e p o t en t i a lap p l i ca t i o n s o f t h e t u n ed s l o sh in g d amp ers i n c lu d e amo n g o th e rs t a l l b u i l d in g s , t o wers ,b r i d g es an d o f f sh o re p l a t fo rms . M o re an a ly t ica l an d ex p e r im en ta l s t ud i e s a re n eed ed t ob e t t e r mo d e l t h e f req u en cy re sp o n se fu n c ti o n o f TSD s t o en su re t h e e f fec t i v e mi t i g a t i o n o ft h e mo t io n s o f b o th ex i s t i n g an d n ew l an d -b ased an d o f f sh o re s t ru ctu re s an d t h e i r c r it i ca ls u b s y s t e m s .

A C K N O W L E D G E M E N T SFin an c i a l a s s i s t an ce p ro v id ed i n p a r t b y t h e PYI-8 4 award t o t h e au th o r u n d e rNa t ional Science Foundat ion Gra nt ECE-8352 223, ma tch ing funds by the severa l indust rials p o n s o rs a n d b y t he T e x a s A d v a n c e d T e c h n o l o g y P r o g r a m u n d e r G r a n t 0 0 3 6 5 22 0 0 - A T Pare gra tefu l ly acknowledged .


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T A B L E I . D E S I G N M O D I F I C A T I O N O F H I G H - R I S E B U I L D I N G SMo d i fy S t ru c tu ra l Sy s t ema. Tr y differe nt structural syste m sb. Ad just s t i f fness & m ass d ist ribut ion to mo di fy m ode shapeChange Building Materiala . Ch an g e f ro m s t eel t o co n c re te o r a co mp o s i t e sy s t emIn c rease Dam p in ga. Di rec t dam ping , e .g ., coat ing dam ping ma ter ia l add part i tion wal l sb . In d i rec t d amp in g

i . Pass iv e co n t ro l, e . g ., t u n ed ma ss d amp ers , t u n ed s l o sh in g d am p ers ,and v iscoelas t ic dam persi i. Ac t ive cont ro l , e .g . , t endon cont ro l , pu lse cont ro l , ac t ive dam pers ,ae ro d y n amic ap p en d ag es an d mass im p ac t

Aero dynam ic Modifica tiona . Aerod ynam ical ly eff ic ien t shapeb . Arch i t ec tu ra l mo d i f i ca t io n , e . g ., ch am fe r in g co m ers , sp o i l e r s, v an es an do p en in g s

Building, Stiffness Ma trix- 1.754

-0 .8 7 70 .00 .00 .0

B

Dia~onal Mass M atr ix[ 0 .45

Tab le II . Bui ld ing Propert ies

-0 .8 7 7 0 .0 0 .0 0 .01 .754 -0 .877 0 .0 0 .0

-0 .8 7 7 1 .7 5 4 -0 .8 7 7 0 .00 .0 -0 .877 1 .754 -0 .8770 .0 0 .0 -0 .8 7 7 0 .8 7 7

x 107

0.45 0.45 0.45 0.45 ] x 106

R E F E R E N C E SA b r a m s o n , H . N . , " T h e D y n a m i c B e h a v i o r o f L i q u i d in M o v i n g C o n t a in e r s ," N A S ASP-106, 1966 .


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Bhuta , P . G. , and Koval , L . R. , "A Viscous Rind Damper for a Free ly Process ingSatell i te," Int ' l . J . Mech. Sci. , Vol. 8, 1966.Bouss inesq , J . , "M emo i r on the Inf luence of Fr ic t ion in the Regu lar Mot ion o f F lu ids ," J .of Math. , Vol . 2, 1868.Ches ter , W. , "Resonan t Osci l la t ions o f Water W aves , " Proc . Royal So cie ty , Vol . 306A,1968.Cok elet , E. D . , "Steep Grav i ty W aves in W ater of Arbit rary Un iform Depth," Phi l . Trans .Ro yal Society, Vol . 286A, 1977.Cooper , R . M . , "Dy namics of Liquids in M oving Conta iners , " J . Am. Rocket Soc ., Vol.30, 1977.Dem irbi lek, Z. , "E nergy Diss ipat ion in Sloshing Waves in a Ro l l ing Rectan gular Tan k - I .M athem at ical The ory," Ocea n Engrg., Vol . 10, No. 5, 1983.Fal t inson, "A Num er ica l Nonl inear Method of S loshing in Tanks w i th Two-Dimens ionalFlow ," J . of Ship Research, Vol . 22, 1978.Fuj ino , Y., e t a l ., "F undam enta l S tudy of Tuned Liquid Dam per (TLD) - A New Dam perfor Bu i ld ing Vibra tions ," Proceedings of the Sym pos ium/W orkshop on Service-abi l i ty of Bui ldings, 16-18 Ma y 1988.Harr is , C. M. and Crede, C. E. (Editors) , Sh ock and Vibrat ion Han dboo k, McG raw-H il lBook Com pany , 1987.Holyer , J . Y . , "Large Ampl i tude Progres s ive In ter f ac ia l Waves , " Journal of F lu idM echan ics , Vol . 93, 1979.Hough, M. A. , "On the Inf luence of Vi scos i ty on Waves and Cur rent s , " Proc . LondonM ath. Society, Vol . 28k, 1897.Kareem , A. , "Latera l -Tors ional M ot ion of Tal l Bui ld ings to W ind Load s , " Journal ofStructural E ngineer ing, ASCE , Vol . 1 11, No. 11, 1985.Kareem , A. , "M i t iga t ion of W ind Induc ed Mot ion of Tal l Bui ld ings ," Journal of WindEng ineer ing and Indust rial A erodyna mics , Vol . 11, 1983.Ka reem , A. , "Win d Effec ts on Structures : A Probabi l i s t ic View point ," Probab i l i s ticEng ineer ing Mecha nics , Vol . 2, No. 4, 1987.Kareem , A. , "W ind-Exci t ed Response of Bui ld ings in Higher Mo des , " J . o f the S t ruct.Div. , ASC E, Vol . 1 07, No. ST4, 1981.

Kareem , A. an d Sun, W . -J . , "S tochas ti c Response of S t ructures wi th F lu id-Conta in ingAp pendag es ," Journal of Sou nd and Vibrat ion, Vol . 11 9, No. 3, 1987.Keel , C . J . and Mahmoodi , P . , "Des ign of Viscoelas t i c S t ructura l Dampers for theColum bia Center Bui ld ing , " Bui ld ing Mot ion in Wind, Edi t ed by N. I syu mo v andT. Tschanz, ASC E, NY, 1986.Ke ulega n, G. R. L . , 1959, "E nergy Dis s ipa t ion in S tanding W aves in Re ctangu larBasins ," J . Fluid Mech . 6. 33.Ki tamura , H. e t a l . , "Des ign and Analys i s of a Tower S t ructure wi th a Tuned MassDam per , " Proceedings , 9 th W or ld Conference on Ear thquake Engineer ing , Tokyo,Japan, 1988.Lam b, H. , Hyd rodynam ics , Dov er Publ ica t ion Inc. , Dover , New York , 1945.Lep elletier , T. G. and Raichlen, F. , "Nonlinear Oscillations in R ectan gular Tan ks," Journalof Enginee r ing Me chanics , ASCE , Vol . 114, No. 1, 1988.M cN am ara, R. J ., "T une d Ma ss Dampers for Bui ldings ," J . of the Structural Div. , ASCE ,Vol . 103 , No. ST9, 1977.M eirovi tch, L. , Com putat ional Me thods in St ructural Dy nam ics , Si j thoff and No ordho ff ,1980.Modi , V. J . and Wel t , F . , "Damping of Wind Induced Osci l l a t ions Through LiquidSloshing," Preprint Vol. 5, Seventh International C onference on W ind Engineering,Aachen, W . Germany , Ju ly 6-10 , 1987.Prospere t ti , A . , 1976, "V iscous Ef fec t s on Sm al l Ampl i tude Sur face Wa ves , " Phys icsFluids 19. 195.


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Sun, Wei-Joe and Kareem, A., "Stochastic Response of Structures with AppendagesContaining Fluids," Dynamic Response of Structures, Edited by G.C. Hart andR.B. Nelson, ASCE, NY, 1980.Tamura, Y., et al., "Wind-Induced Vibration of Tall Towers and Practical Applications ofTuned Sloshing Damper," Proceedings of the Symposium/Workshop onServiceability of Buildings, 16-18 May 1988.Verhagen, J. H. G., and Wijngaarden, V. L., "Nonlinear Oscillations of Fluid in aContainer," Journal of Fluid Mechanics, Vol. 22, 1965.Wiesner, K. B., "Taming Lively Buildings," Civil Engineering, ASCE, June 1986.


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k j C j

k 2 C 2

k I C 1

Fig. 1 . Mechanical M odel of S losh ing Flu id

Fi g . 2 . M od e l o f F l u id an d S tructura l S ys tems


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Kb k~M b ~ - ~ ~ ~ x3(t)

-" '---- '~3 ~ X (t) I L , ~ aCb ~ x l ( t )

I .( t )Fig. 3 . Equivalen t Mo del of the Build ing and the Fluid System

3e-8

r. .) ~ '.e-8

~ ~r~ le-8

[ . . .oe+0 I l l F " "

0 .9

![]

|

.0F / F B

i iNO WATER4% DAMPINGI

1.1 1.2

Fig . 4. Trans fer Function of Build ing - TSD System


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5e-9Z~ " " 4 e - 9p . , Z

e-O

~ ~ 2 e - 9

Z~ l e - 9

Documents

[2](1990)Reduction of Wind Induced Motion Utilizing a Tuned Sloshing Damper