Time-domain Aeroelastic Analysis of Bridge using a Truncated Fourier Series of the Aerodynamic Transfer Function
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1 Te 8 Ci-Jp-ore eriol Worksop o Wid Egieerig My, 3 Time-domi Aeroelsic Alysis of ridge usig Truced Fourier Series of e Aerodymic Trsfer Fucio Jiwook Prk, Seoul iol iversiy, ore ilje Jug, iversiy of ore Dme, SA Ho-yug im, Seoul iol iversiy, ore He Sug Lee, Seoul iol iversiy, ore
2 Coes. roducio. Cusliy Requireme 3. Truced Fourier Series Approximio 4. Applicio d Verificio - H-ype secio 5. Summry Seoul iol iversiy
3 . roducio Aerodymic Forces iduced by Moio of ridge - Self-exied forces L e Aerodymic Sysem M e Srip Teory Goverig Equio : vier-sokes Eq. egrio of e Pressure Disribuio o lyicl soluios of e erodymic forces sully ssumed s lier sysem i frequecy domi Deermied roug Wid uel es or CFD simulio For e ime-domi lysis, e erodymic sysem sould sisfy e Cusliy Requireme. Seoul iol iversiy 3
4 4 Seoul iol iversiy Lierized Aerodymic Sysem i Frequecy Domi - Adopig e Fluer Derivives proposed by Scl Mixed frequecy/ime domi Smll-mpliude siusoidl moio wi sigle frequecy were, : Reduced frequecy siclly bsed o e Aerodymic Trsfer Fucios were, F : Fourier rsform A A H H A A H H M L e e F F F F A ia A ia H ih H ih M F L F e e. Cusliy Requireme
5 Mesured Trsfer Fucio ormlized mgiude. Cusliy Requireme Lierized Aerodymic Sysem i Time-domi - sig Covoluio egrl Teorem y kig e iverse Fourier rsform L M e e d d d d -5 Aerodymic mpulse Respose Fucios - mgiry pr Rel pr -5 =/ 3 4 Seoul iol iversiy i e d for k, l, verse FT 4 Evlued RF = : Cusliy codiio / 5
6 ormlized mgiude. Cusliy Requireme Cusliy Codiio - Defiiio for 4 Evlued RF Modified RF - Memicl meig Oe-sided covoluio egrl L M e e d d / d d Reliosip bewee e rel d imgiry pr of TF R cos si d for - Pysicl meig o erodymic force is geered before e deck moves Seoul iol iversiy 6
7 Rel pr of compoe. Cusliy Requireme Previous works - RFA Riol Fucio Approximio : RFA is bsed o e soluio o e idelly i secio. : RFA s limiio o is pplicbiliy o bluff secios. - Pely Fucio Approc, Jug e l. : is pplicble o e bluff secios : Cusliy codiio is wey imposed s pely fucio roug e opimizio. -Limiio of RFA, Jug e l. Mesured rsfer fucio RFA r= RFA r= RFA r=3 4 - Aerodymic rsfer fucio for H-ype secio - RFA is drw gis e rig vericl xis RFA yields urelible resuls / Propose e efficie meod excly sisfy e cusliy codiio!! * Jug,., im, H.., d Lee, H. S.. Evluio of impulse respose fucios for covoluio iegrls of erodymic forces by opimizio wi pely fucio. J. Eg. Mec., 385, Seoul iol iversiy 7
8 . Cusliy Requireme Compriso bewee Previous Work d Proposed Meod RFA Proposed Approximio meod Ryleig-Riz ype pproximio Fiie eleme meod Ryleig-Riz ype pproximio sis fucio Riol fucio Cubic splie Sie, Cosie fucio Cusliy codiio Srogly eforceme Wey eforceme Srogly eforceme Applicbiliy Limiio of pplicio o e bluff secio Applicble o e bluff secio Applicble o e bluff secio Seoul iol iversiy 8
9 3. Truced Fourier Series Approximio Approximio usig Truced Fourier Series - Fourier series represeios of e rsfer fucios R b cos mx bsi mx, b mx : modified rsfer fucio : coefficies of e Fourier series : e umber of erms i e Fourier series : mximum reduced frequecy - eed of e lier erm b i e imgiry pr Wiou e lier erm, e discoiuiy rises mx. Te discoiuiy cuses Gibbs peomeo. A lrge umber of erms sould be icluded. mx Seoul iol iversiy 9
10 3. Truced Fourier Series Approximio Eforceme of e Cusliy Codiio - RF correspodig o e modified rsfer fucio : RF becomes series of Dirc-del fucios. R [ cos R cos b si d si mx b ] d mx b - Cusliy codiio for e modified rsfer fucio for b for,, Seoul iol iversiy
11 Seoul iol iversiy Fil Aerodymic Forces mx mx mx mx e e b b M b b L e e d d M d d L To perform e covoluio iegrls, oly ps displcemes re required. 3. Truced Fourier Series Approximio
12 3. Truced Fourier Series Approximio Deermiio of Coefficies of e Fourier Series - Te ukow coefficies re deermied by miimizig e errors bewee e mesured d modified rsfer fucios. Mi w : weigig fcor, R, R L mx mx w R R w d L : L -orm, : mesured rsfer fucios ierpoled by cubic splie L d b T : + ukows : + equios Seoul iol iversiy
13 4. Applicio d Verificio - H-ype secio Codiio of e Problem - Jug el l. demosred e limiio of RFA for is H-ype secio - Goverig equio m c k L m c k e M L e ex M ex m c k f 3.64 kg/m,.3 kg/s/m, 33.6 /m/m, k 3.5 Hz, m c f. kgm /m. kgm /s/m 6. m/m 5.5 Hz - Dimesio of e H-ype bluff secio, im d ig 7 6m/ s 3.5 kg/m - Exerl forces : To compre e sedy-se resposes wi ose obied by mesured rsfer fucio. L M ex ex /m si m/m ex, ex 8 rd/s Seoul iol iversiy 3
14 mgiy pr of compoe Rel pr of compoe 4. Applicio d Verificio - H-ype secio Compoes of e Trsfer Fucios for e Lif Force - Mesured rsfer fucio Proposed meod = Proposed meod =5 Proposed meod = =/ R Mesured rsfer fucio - Proposed meod = Proposed meod =5 Proposed meod = =/ - Te d Proposed meod yields lmos e sme resuls. - Eve, e Proposed meod yields closer soluio o e Mesured e. - For e proposed meod, oly 5 erms of Fourier series re eoug coverge. Seoul iol iversiy 4
15 mgiry pr of compoe Rel pr of compoe 4. Applicio d Verificio - H-ype secio Compoes of e Trsfer Fucios for e Lif Force Mesured rsfer fucio Proposed meod = Proposed meod =5 Proposed meod = R Mesured rsfer fucio Proposed meod = Proposed meod =5 Proposed meod = =/ =/ - Te d Proposed meod yields lmos e sme resuls. - Te differeces wi Mesured idices e degrees of violio of e cusliy codiio i e Mesured. Seoul iol iversiy 5
16 mgiry pr of compoe Rel pr of compoe 4. Applicio d Verificio - H-ype secio Compoes of e Trsfer Fucios for e Mome 4 4 R Mesured rsfer fucio - Proposed meod = Proposed meod =5 Proposed meod = =/ Mesured rsfer fucio - Proposed meod = Proposed meod =5-4 Proposed meod = =/ -Te resuls for e mome c be similrly ierpreed wi ose for e lif force Seoul iol iversiy 6
17 mgiry pr of compoe Rel pr of compoe 4. Applicio d Verificio - H-ype secio Compoes of e Trsfer Fucios for e Mome 4 Mesured rsfer fucio Proposed meod = Proposed meod =5 Proposed meod = 4 R =/ Mesured rsfer fucio - Proposed meod = Proposed meod =5 Proposed meod = =/ -Te resuls for e mome c be similrly ierpreed wi ose for e lif force Seoul iol iversiy 7
18 Priculr sol. Vericl displceme cm Priculr sol. Roiol gle - rd Vericl displceme cm Priculr sol. Roiol gle - rd 4. Applicio d Verificio - H-ype secio Resposes - sig ewmrk-be meod wi ime iervl of.96 sec - Te, proposed meod d priculr soluio ve o oiceble differece. 5 Proposed meod = 5 Proposed meod = -5 Time s 5 Priculr sol. Proposed meod = -5 5 Time s Priculr sol. Proposed meod = Time s Time s Seoul iol iversiy 8
19 4. Applicio d Verificio - H-ype secio Compriso of Compuio Time - Compuer:.4GHz sigle core - Progrm: MATLA Rb - Alysis ime: sec - Time iervl:.958 sec Proposed meod = Compuio ime 4.7 sec.6 sec Reducio of 94 % Proposed meod c be used o perform ime-domi eroelsic lysis eve for lrge-scle srucure efficiely wiou y loss of ccurcy. Seoul iol iversiy 9
20 5. Summry Cusliy Requireme Propose e Exc d Efficie Meod usig Truced Fourier Series - Cusliy codiio is srogly imposed. - RF becomes Dirc-del fucios Reducio of e compuio Applicio d Verificio roug e exmple of H-ype bluff secio Seoul iol iversiy
21 ACOWLEDGEMET Tis reserc ws suppored by e gr 9CCT- A from e Miisry of Ld, Trspor d Mriime Affirs of ore goverme roug e Core Reserc siue Seoul iol iversiy for Core Egieerig Tecology Developme of Super Log Sp ridge R&D Ceer. Tk you!
Time-domain Aeroelastic Analysis of Bridge using a Truncated Fourier Series of the Aerodynamic Transfer Function
Time-domai Aeroelasic Aalysis of ridge usig a Trucaed Fourier Series of he Aerodyamic Trasfer Fucio Jiwook PA Graduae Sude Seoul aioal iversiy Seoul, orea jwpark7@su.ac.kr H Sug LEE Professor Seoul aioal
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