IDENTIFICATION OF NONLINEAR DAMPING AND STIFFNESS OF SPRING-SUSPENDED SECTIONAL MODEL

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1 The Eighh Asi-Pcific Conference on Wind Engineering, December 1 14, 13, Chenni, Indi IDENTIFICATION OF NONLINEAR DAMPING AND STIFFNESS OF SPRING-SUSPENDED SECTIONAL MODEL Gung-Zhong Go 1, Le-Dong Zhu, Qun-Shun Ding 3 1 PhD Cndide of Deprmen of Bridge Engineering, Tongji Universiy, Shnghi 9, Chin, gungzhonggo88@gmil.com Professor of Se Key Lborory of Disr Reducion in Civil Engineering / Key Lborory for Wind Resisnce Technology of Bridges of Minisry of Trnspor / Deprmen of Bridge Engineering, Tongji Universiy, Shnghi 9, Chin, ledong@ongji.edu.cn 3 Associed Professor of Se Key Lborory of Disr Reducion in Civil Engineering / Key Lborory for Wind Resisnce Technology of Bridges of Minisry of Trnspor / Deprmen of Bridge Engineering, Tongji Universiy, Shnghi 9, Chin, qsding@ongji.edu.cn ABSTRACT A prospecive mehod is developed o improve he mesuremen precision of lf-excied force in cionl model es. The mesured lf-excied force for recngulr cross cion wih deph-widh rio 1: hs significn nonliner chrcerisics. For spring-suspended bluff cionl model, srucurl nonlineriies re no ignorble in governing equion of moion; becu of he wek nonliner chrcerisics of lf-excied force. An equivlen linerizion mehod is doped o model he dded dmping nd siffness effec vi free decy respon in zero wind speed condiion. I is found h he nonliner chrcerisics of dded dmping effec re rher obvious, while h of dded siffness effecs is considerbly wek. Employing implici Newmrk-β inegrion mehod, numericl vlidion procedure is crried ou o verify he propod idenificion mehods. The clculed resuls gree quie well wih ed ones. This rerch work hs significn pplicions for furher sudy of nonliner undy wind induced insbiliies. Keywords: Spring-suspended cionl model, Nonliner dmping, Nonliner siffness, Undy glloping 1 Inroducion The eroelsic phenomen cud by inercion beween pssing wind nd srucure hs been subjec of ineres o civil engineers since he collp of old Tcom Nrrows Bridge in 194s. Erly experimens by Prkinson (1989), Osuki (1974), Bermn (1987) nd Bouclin (1977) e l demonsre h slender elsic srucure wih erodynmiclly bluff cion is prone o glloping, which hs srong nonliner nd undy chrcerisics. To review he cul mechnism of glloping, i is necessry o mesure nonliner erodynmic force wih high precision in wind unnel es. For civil engineering srucures wih bluff cions, undy glloping is lwys excied in he low wind speed region; s resul, lfexcied force is verl orders of mgniude smller hn ineril force of he srucure ilf. In convenionl cionl model es, force blnces re pu he end of cionl model o direcly mesure ol force. Since he ineril force ccouns for lrge proporion of mesured ol force, he precision of lf-excied force remins relively low. In his sudy, he echnique of inernlly-plcing force blnces ino cionl model is developed o ge high-precision lf-excied force, i.e. he cionl model is designed ino wo pre prs: ouer co pr nd inner frme pr, he wo prs re conneced by force blnces. The mesured force only consiss of ineril force of ouer co pr nd lf-excied force, nd he precision of lf-excied force will be lrgely improved (Zhu e l 1). Proc. of he 8h Asi-Pcific Conference on Wind Engineering Ngesh R. Iyer, Prem Krishn, S. Selvi Rjn nd P. Hrikrishn (eds) Copyrigh c 13 APCWE-VIII. All righs rerved. Published by Rerch Publishing, Singpore. ISBN: doi:1.385/

2 Proc. of he 8h Asi-Pcific Conference on Wind Engineering (APCWE-VIII) Convenionlly, forced nd free vibrions re boh bsic es mens o sudy undy glloping (Bermn e l 1987, Bouclin 1977, Osuki 1974, Prkinson 1989, Simiu 1996). However, he inercion mechnism beween fluid nd srucure is olly differen for he wo mehods. For free vibrion es, he undy fluid field excies srucure o vibre, nd he vibrion of srucure will furher influence he flow pern bck; hus he influence of domine erodynmic nonliner fcor will be grdully mplified in he process of vibrion. While in he c of forced vibrion, he behvior of cion model is conrolled by mechnicl driving sym; he disurbed fluid field by he moion of cionl model cn no in urn influence he model vibrion, herefore he inercion mechnism is incomplee in forced vibrion. I remins quesionble wheher forced vibrion is pplicble in sudying undy glloping or no. In his sudy, forced nd free vibrion ess wih he sme bluff cionl model re crried ou. Experimen resuls re compred nd conribue o beer undersnding of nonliner undy glloping phenomenon. From noher perspecive, for spring-suspended cionl model undergoing undy glloping, boh srucurl nd erodynmic nonlineriies will inevibly led o nonliner oscillion phenomenon. Since he erodynmic nonlineriy is rher wek for undy glloping, he srucurl nonlineriies re no ignorble when free-oscillion es is employed. I hs been proved h he vibrion sym prmeers (i.e. dmping nd frequency) re nonliner funcions of vibrion mpliude o some exend, even if he elonged springs re rher liner over he enire rnge of oscillion. Go e l. (13) buil up heory o idenify mpliude dependency of dmping nd frequency of spring-suspended cionl model in zero wind speed condiion. The idenified nonliner dmping nd frequency involves ll nonliner fcors including erodynmic force cing on he model in zero wind speed, i.e. dded dmping nd dded siffness(or equivlenly, dded mss) effecs. In governing equion of moion for non-zero wind speed condiions, dmping nd frequency prmeers should no include dded dmping nd dded siffness effecs. In considerion of nonliner erodynmic effec of bluff cion, dded dmping nd dded siffness effecs in zero wind speed will definiely be nonliner. In his sudy, n equivlen linerizion mehod is developed o idenify he dded dmping nd siffness nonlineriies in spring-suspended free vibrion sym from free decy respon wih n iniil exciion in zero wind speed condiion. Then he effecive dmping nd siffness erm in governing equion of moion for non-zero wind speed condiions cn be obined by excluding dded dmping nd siffness from idenified ol dmping nd siffness. In summry, his pper propos new perspecive o clrify source of nonlineriies for bluff cionl model. Firsly, new cionl model es echnique is employed o ge high-preci nonliner lf-excied force. Nex, he srucurl nonlineriies in springsuspended sym re modeled by removing he influence of erodynmic force in zero wind speed condiion. This rerch lys significn foundion for furher sudying undy glloping phenomenon. Comprison of forced nd free vibrion ess.1 Secionl model wih inernlly-plced force blnces A ypicl recngulr cion model wih deph-widh rio 1: is doped o invesige undy glloping. To ge high-ccurcy lf-excied force direcly, he ouer co pr of he middle gmen in Fig.1 is conneced o he frme pr by pir of high nsiive piezoelecric dynmic blnces; dynmic displcemen nd ccelerion re mesured simulneously ogeher wih he dynmic forces. Fig.1 shows schemic up of he spring-suspended free vibrion es (wo end ples no shown). The cionl model hs 64

3 Proc. of he 8h Asi-Pcific Conference on Wind Engineering (APCWE-VIII) lengh of 1.665m, wih 5mm deep nd 1mm wide. The ol mss of cionl model is 6.98kg, nd he mss of co pr of middle gmen is only.448kg. Fig. displys deiled rrngemen of cross cion (connecions beween blnce nd cloh pr or frme pr re shown schemiclly). In he process of oscillion, he pir of force blnces mesure ineril force nd erodynmic force of he co pr of middle gmen. The governing equion of moion of co pr of middle gmen cn be described s mx f f ms (1) where m is mss of co pr of middle gmen, fms is summion of mesured force, f is ol lf-excied force cing on he co pr. Since he mss of co pr is much lower hn he ol mss of cionl model, lfexcied force ccouns for considerbly lrge proporion of mesured force. In forced vibrion es, he rrngemen of cionl model is kep he sme, only he springs nd rms re replced by mechnicl driving sym plced ouside of TJ-1 wind unnel.. Comprison of forced nd free vibrion es resuls In spring-suspended free vibrion es, ypicl undy glloping phenomenon is obrved. The cionl model exhibis limi cycle oscillion (LCO) in unsble region (Fig.4). Fig.5 illusres displcemen nd lf-excied force digrm when vibrion mpliude becomes sble, indicing significn nonliner feures, nd Fig.6 depics he mpliude specrum of lf-excied force in sble region, where he lf-excied force hs significn higher order hrmonic componens. Fig.7 shows ime hisory of insnneous frequency, indicing significn frequency modulion effecs, which is cler indicion of nonliner effec of oscillion. f 1 ms f 1 ms f mx? f ms rnsver siffening ple f ms Z Y Force Blnce Side Segmen Mid Segmen Side Segmen X Arm Spring wooden ple mel frme force blnce mel frme co pr frme pr Fig.1 Schemic of experimen up Fig. Arrngemen of cross cion Fig.3 Secionl model in TJ-1 wind unnel Fig.4 Displcemen of undy glloping The forced vibrion es gives compleely differen resuls. The higher order componens of lf-excied force lmos dispper (Fig.6 (b)). Furhermore, incresing wind speed nd vibrion mpliude leds o lile chnge in higher order componens. Fig.5 (b) 65

4 Proc. of he 8h Asi-Pcific Conference on Wind Engineering (APCWE-VIII) shows displcemen nd lf-excied force digrm when vibrion mpliude is kep 8mm, indicing lmos liner relionship, nd similr resuls will be obined if he vibrion mpliude incres s lrge s o mm or vibrion frequency chnges. Fig.7 (b) displys ime hisory of insnneous frequency, he frequency modulion effec is due o imperfec conrol precision of forced vibrion driving sym, which is compleely differen from he free vibrion c. free vibrion Fig.5 Comprison of x (b) forced vibrion f s ph digrm f free vibrion (b) forced vibrion Fig.6 Comprison of f specrum free vibrion (b) forced vibrion Fig.7 Comprison of frequency modulion effec Then why re es resuls so inconsin by free nd forced vibrion? I ems o sugges h he formulion of nonliner oscillion of undy glloping relies hevily on fluid-srucure feedbck sym, where fluid nd srucure need o inerc freely wih ech oher o form he feedbck mechnism. This is indeed he fundmenl mening of lfexcied vibrion or eroelsic phenomenon. I comes no surpri o find h he fluid force cing on he sme cionl model displys compleely differen properies. The forced vibrion sym is likely no pplicble o sudy nonliner undy fluid-srucure inercion 66

5 Proc. of he 8h Asi-Pcific Conference on Wind Engineering (APCWE-VIII) phenomen. Bd on he ess resuls nd nlys bove, free vibrion echnique is chon o furher sudy undy glloping. 3 Governing equions of moion for free vibrion es For spring-suspended sym depiced in Fig.1, governing equion of moion in smooh flow field cn be described s Mx S( (,) x x F where M is ol effecive mss of vibrion sym, Sxx (,) is nonliner force in he mechnicl sym, which cn be ssumed o hve negligible memory effec nd expresd s funcion of curren moion. F is he ol erodynmic force cing on he cionl model. The nonliner force Sxx (,) cn be furher divided ino wo prs ccording o is effecs on he vibrion sym Sxx (,) Dxx (,) Kxx (,) (3) where Dxx (,) is effecive nonliner dmping force erm, which is no in ph wih displcemen x nd s resul dissipes mechnicl energy. Kxx (,) is effecive nonliner resoring force erm, which is in ph wih displcemen x nd s resul only influences he frequency of vibrion sym. As discusd bove, for flowing ir condiions, erodynmic force hs been ken ino ccoun by F erm in Eq.. On he oher hnd, modl prmeers of spring-suspended vibrion sym is usully idenified by free decy respon in zero wind speed condiion, which mens he dded siffness (or equivlenly dded mss) nd dded dmping effec will be inevibly incorpored. Then he idenified mechnicl force erms should exclude nonliner dded siffness nd dded dmping force respecively. Dxx (,) D (,) xx D (,) xx (4) Kxx (,) K xx K (,) (,) xx (5) where D (,) x x is idenified nonliner dmping force in zero wind speed, which involves ll dmping fcors in he vibrion sym, D (,) x x is he dded dmping force in zero wind speed, which reprens nonliner dmping effec of fluid on cionl model; K (,) x x is idenified nonliner resoring force in zero wind speed condiion, which involves ll frequency-influencing fcors, K ( x, x) is dded siffness in zero wind speed condiion, which reprens nonliner effec of surrounding fluid on frequency of cionl model. The relionship beween f in Eq.(1) nd F in Eq. re s follows: F f (6) where is he rio of middle gmen lengh o ol lengh of cionl model. In he process of free vibrion es, dynmic displcemen x, ccelerion x nd forces fsc re simulneously mesured. Then high-precision erodynmic force f cn be bined by Eq.(1). Inring f ino Eq.(6), high-precision erodynmic force F cing on he whole cionl model will be clculed. The nex p is o clrify nd model he nonlineriies in mechnicl properies in Eq.. Combine Eq.(3), Eq.(4) nd Eq.(5), i cn be found h i is necessry o model ol mechnicl force erms D (,) x x, K (,) x x nd dded mechnicl force erms D (,) x x, K ( x, x) respecively. Since he uhor hs buil heory o model D (,) x x nd K (,) x x erms (Go e l,13), wh follows in his pper minly focus on he idenificion heory of dded dmping force D (,) x x nd dded siffness K (, ) x x in zero wind speed condiion. 67

6 Proc. of he 8h Asi-Pcific Conference on Wind Engineering (APCWE-VIII) 4 Equivlen linerizion mehod for idenifying nonliner dded dmping nd siffness Eq. ~ Eq. (5) demonsre h i is necessry o model nonliner dmping nd siffness propery in he spring-suspended free vibrion sym. Nonliner mechnicl propery idenificion problem hs been widely sudies, bu sill no well solved, which should be ribued o is complex physicl sources. The physicl sources of nonliner mechnicl propery in spring-suspended free vibrion sym cn be clssified ino he following cegories: 1) Elsic hyresis effec in springs, rms nd mel frme of cionl model; ) Fricion joins, connecions nd inerfces; 3) Nonliner forces by surrounding fluid on cionl model, rms, spring, ec. The complex physicl sources of nonliner mechnicl propery mke i imprcicl o consruc he nonliner dmping nd siffness direcly from physicl menings. However, if he mechnicl propery cn be ssumed o keep sble in he process of experimen, hen i cn be modeled in n indirec wy. In his sudy, he widely ud Equivlen Linerizion Mehod (ELM) in he heory of nonliner vibrion (Nyfeh & Mook 1979) is ud o pproxime Eq. by he following linerized equion: Mx D( ( ) x K ( ) x F (7) where is he equivlen mpliude. x x / (8) x x/ where is he insnneous circulr frequency, which cn clculed from displcemen ime hisory hrough HHT mehod or he ime domin lgorihm propod by he uhor. Then equivlen expression of Eq. (4) ~ Eq. (5) cn be obined: D D D (9) K K K (1) The bove nonliner mechnicl prmeers re idenified vi free decy respon in zero wind speed condiion. Among hem, ol dmping erm D nd ol siffness erm K cn be idenified by displcemen free decy respon (Go e l 13). Added dmping erm D nd dded siffness erm K cn be idenified vi force blnces respon in zero wind speed condiion. Similr o he procedure in non-zero wind speed condiions, erodynmic force should be firsly obined by removing ineril force from mesured force, s indiced in Eq.(1). Noing h in zero wind speed condiion, oscillory cionl model is ffeced by is surrounding ir, jus s h in non-zero wind speed condiions, so i is resonble o u he erm lf-excied force in boh siuions. 4.1 Added dmping idenificion mehod In he process of free decy vibrion wih n iniil exciion in zero wind speed condiion, ol dissipion of mechnicl energy by erodynmic force cn be expresd s where f W f xd (11) f is lf-excied force cing on he middle gmen in free decy vibrion, x is velociy ime hisory of cionl model, which cn be obined wih discree difference mehod bd on smpled displcemen signl. According o he philosophy of ELM, ph effec is higher order smll quniy compred o mpliude effec on mechnicl energy dissipion in wekly nonliner sym. So ph effec cn be verged ou by geing he rend of W : 1 polynomil fi W Wv W d d (1) 68

7 Proc. of he 8h Asi-Pcific Conference on Wind Engineering (APCWE-VIII) According o he lw of conrvion of energy, he power of he work of erodynmic force equls he power of mechnicl dissipion: Pv dwv / d (13) From noher perspecive, he verge power of he work of erodynmic force cn lso be inerpreed s verge work done in period: v ( ) P D x d D (14) Combing Eq. (13) nd Eq. (14), dded dmping erm D cn be expresd s: ( dw M D ) v (15) d E where E is he insnneous ol mechnicl energy of spring-suspended sym. The dded dmping coefficien cn be furher expresd ino viscous dmping coefficien form: D (16) M To furher minimize idenificion error, bove idenificion process should be conduced verl imes by repeedly free decy he model in zero wind speed condiion; finl dded dmping coefficiens should be he les squre fi of he idenified resuls. 4. Added siffness idenificion mehod The dded siffness erm K cn be idenified hrough wo differen wys. 1) Inegrion-verge idenificion mehod The dded resoring force cn be pproximed by removing dded dmping force from ol erodynmic force. K x f D x (17) Similr o dded dmping force, ph effec is lso higher order smll quniy compred o mpliude effec on vibrion frequency. Averge he ph effec on he lef side of Eq. (17) K ) ( verged lef side K ) x d K ( (18) Averge he ph effec on he righ side of Eq. (17) by polynomil fiing nd derivion. verged righ side f x D xx v (19) Combing Eq. (17),Eq. (18) nd Eq. (19), dded siffness erm K cn be expresd s: f x D xx x v K ) ) Aerodynmic force-displcemen digrm idenificion mehod In he process of free decy vibrion, if displcemen x reches is mxim or minim, he velociy x is definiely zero. Assuming memory effec is negligible in he mechnicl vibrion sym, zero velociy corresponds o zero insnneous dmping force. Then ries of pure dded resoring force nd corresponding mpliude cn be go from erodynmic nd displcemen digrm, by picking mxim nd minim of displcemen x nd corresponding erodynmic force f. The funcionl relionship of displcemen nd resoring force chieved by polynomil fiing he discree pek poins [ ( ), f resore )] obined bove. For specific mpliude, he slope of ngen line of he polynomil funcion is he dded siffness coefficien K. 69

8 Proc. of he 8h Asi-Pcific Conference on Wind Engineering (APCWE-VIII) Afer obining he dded siffness erm K, equivlen dded frequency cn be defined s: 1 K f (1) M To furher minimize idenificion error, bove idenificion process lso should be conduced verl imes; finl dded siffness coefficiens should be he les squre fi of he idenified resuls. 5 Nonliner dded dmping nd dded siffness of cionl model In he process of free decy vibrion wih n iniil exciion in zero wind speed condiion, comprison of work done by erodynmic force nd ol dissipion of mechnicl energy re shown in Fig.8, he mechnicl energy consumed by dded dmping effec kes lrge proporion in ol dissipion of mechnicl energy. Furhermore, idenified ol nd dded dmping rio re displyed in Fig.9, s cn be en, boh ol nd dded dmping rio re nonliner funcions of mpliude, proving he necessiy of idenifying nonliner dmping effec. The pr beween he wo curves in Fig.8 reprens he effecive dmping rio in Eq.(7). Fig.1 shows he comprison of dded siffness idenificion resuls by wo propod mehods, nd he resuls re in firly good greemen, confirming he pplicbiliy of propod idenificion mehods. Differen from dmping rio in Fig.9, he nonlineriies of ol siffness nd dded siffness of cionl model re considerbly wek in Fig.1, which my due o he fc h nonliner resoring force in cionl model vibrion sym is smll compred wih liner resoring force provided by elonged springs. Fig.11 demonsres he displcemen nd erodynmic force ph digrm in he process of free decy. I cn be en clerly h he shpe nd rend of hyreic loops chnges drmiclly during he mpliude developing sge, indicing he chnge of dded dmping nd siffness. Discree pek poins[, f resore )] re lso shown in Fig.11. resore Fig.8 Dissipion of mechnicl energy Fig.9 Tol dmping nd dded dmping Fig.1 Idenified equivlen dded frequency Fig.11 x f ph digrm 7

9 Proc. of he 8h Asi-Pcific Conference on Wind Engineering (APCWE-VIII) 6 Experimenl verificion A numericl vlidion procedure will be crried ou in he following prgrph o verify he propod idenificion mehod in his pper. Firsly, idenified lf-excied force ime hisory is depiced in Fig.1 in non-zero wind speed condiion; As cn be en, he mpliude of lf-excied force is bou 1%~% of mesured force by force blnces nd he precision cn be improved when u Eq.(1) o obin lf-excied force. In ddiion, he curve shpe of erodynmic force is disored from sine wve, which indices he nonliner erodynmic propery of recngulr cion. The bsic checking rule is h idenified effecive dmping nd siffness ogeher wih high-precision erodynmic force should sisfy Eq.(7), i.e. sisfy equilibrium condiion in every momens. Since we cre more bou displcemen respon in prcicl pplicion, more rigorous rule is ud o check he displcemen respon ime hisory wih experimenl resuls. Implici Newmrk-β mehod is employed o numericlly inegre Eq.(7). The iniil ime is chon s cerin smpled ime poin when displcemen reches is pek respon nd iniil velociy equls zero. Fig.13 shows he comprison of clculed nd ed displcemen ime hisory. The clculed resuls re lile bi smller hn he ed one during developing sge, nd gree quie well during sble sge. Fig.1 Deil view of force componens Fig.13 Clculed displcemen ime hisory 7 Conclusions This sudy hs inroduced some new perspecives bou how o sudy undy glloping phenomen in wind unnel es. Firs of ll, by pring he ouer co pr from frme pr nd mesuring he ol force of co pr only, he precision of lf-excied force mesuremen will be grely improved. Then spring-suspended free vibrion nd forced vibrion ess re underken respecively, nd he inconsince of es resuls indices h he formulion of nonliner undy glloping rely hevily on fluid-srucure feedbck sym; forced vibrion is likely o be inpplicble for sudying nonliner undy glloping. For spring-suspended free vibrion, i is necessry o exclude dded dmping nd dded siffness (or equivlenly, dded mss) effecs from ol dmping nd siffness idenified from free decy respon in zero wind speed condiion. Clssicl equivlen linerizion mehod is doped o model he nonliner dded dmping nd dded siffness effecs. Idenificion resuls indice h boh dded dmping nd dded siffness re nonliner nd cn be expresd s nonliner funcions of mpliude. I is found h he 71

10 Proc. of he 8h Asi-Pcific Conference on Wind Engineering (APCWE-VIII) nonliner chrcerisics of dded dmping effec re rher obvious, while h of dded siffness effecs is considerbly wek. The relibiliy of propod idenificion mehod is verified by implici Newmrk-β inegrion mehod, he clculed displcemen is in good greemen wih experimen over he whole smpled ime hisory. 8 Acknowledgemen The work described in his pper ws suppored by he Nionl Nurl Science Foundion of Chin (Grn nd 91153). Any opinions nd concluding remrks prened in his pper re enirely ho of he wriers. References Bermn, P. W., Grshore,I.S., Mull,D.J. nd Prkinson,G.V.(1987), Experimenl on flow-induced vibrion of squre-cion cylinder, J. Fluid nd Sr., 1, Bouclin, D.N. (1977), Hydroelsic insbiliy of squre cylinders, J. Sound Vib., 9, Nyfeh A. H., Mook D. T. (1979), Nonliner oscillions, John Wiley & Sons, New York, USA. Osuki,Y., Wshizu,K., Tomizw,H. nd Ohy,A.(1974), A noe on he eroelsic insbiliy of prismic br wih squre cion, J. Sound Vib., 34, Prkinson,G.V.(1989), Phenomen nd modelling of flow-induced vibrions of bluff bodies, Prog. Aerospce Sci., 6, Simiu, E. nd Scnln, R. H. (1996), Wind Effecs on Srucures, 3 rd Ediion, John Wiley & Sons, New York, USA. Zhu L. D., Meng X. L., Guo Z. S.(1), A novel empiricl non-liner model for vorex-induced force on clod box brige deck, The Sevenh Inernionl Colloquium on Bluff Body Aerodynmics nd is Applicion (BBAA7), Shnghi, Chin, Sepember -6, 1. Go G.Z., Zhu L. D., Wu H. (13), Idenificion of ol nonliner dmping nd frequency of spring-suspended cionl model, The 15 h Nionl Conference on Srucurl Wind Engineering nd The 1 s Nionl Forum on Wind Engineering for Grdue Sudens, Chengdu, Chin, July 9- Augus 3, 13.(in Chine) 7