Computation of Aerodynamic Forces for LongSpan Bridges 3文档格式.docx
- 文档编号:21058092
- 上传时间:2023-01-27
- 格式:DOCX
- 页数:28
- 大小:26.06KB
Computation of Aerodynamic Forces for LongSpan Bridges 3文档格式.docx
《Computation of Aerodynamic Forces for LongSpan Bridges 3文档格式.docx》由会员分享,可在线阅读,更多相关《Computation of Aerodynamic Forces for LongSpan Bridges 3文档格式.docx(28页珍藏版)》请在冰豆网上搜索。
A
Becauseofthehighflexibilityandrelatively
lowstructuraldamping,long-spanbridgesare
pronetowind-inducedvibration.Dynamicre2sponseofabridgesubjectedtostochasticwind
loadscanbestudiedeitherinthefrequencydo2mainorinthetimedomain.Basedonthestochas2ticvibrationtheory,Davenport[1]firstdeveloped
anapproachforwindresponseanalysisinfre2quencydomainconsideringbuffetingloadsonly.
Onthisbasis,SimiuandScanlan[2]establisheda
theoreticalframeworkforanalysisofbothbuffet2ingandflutteringresponsesinthefrequencydo2mainbyuseoftheaerodynamicderivativescon2ceptandthequasi-steadytheory,inwhichboth
buffetingandself-excitedforcesweretakeninto
consideration.Thefrequencydomainmethod
mentionedaboveisbasedonthelinearhypothesis
Receiveddate:
April2,2001
3Foundationitem:
TheHighwaysDepartment,HongKong
Government,andtheNaturalScienceFoundationof
GuangdongProvince(980634)
Biography:
SuCheng(bornin1968),male,associate
professor,Ph.D.,mainlyresearchesoncomputational
mechanics,tallbuildingstructuresandlong-spanbridges.
andthetotalresponsecanbeobtainedbyasuper2positionofthecontributionsfromallthevibra2tionmodes.Thisassumption,however,isnotap2propriateinthecaseoflong-spanbridges,be2causeoftheirhighflexibilityandthus,nonlinear2ityduetoeithergeometricoraeroelasticeffects
mustbeconsidered.Alternatively,nonlinearre2sponseoflong-spanbridgescanbeanalyzedin
timedomainbyusingthestep-by-stepnumerical
integrationtechniques[3,4].
Toperformwind-inducedvibrationanalysis
bytimedomainapproach,onewillrequirewind
velocitytimehistoriessimulatedatlocationsalong
thebridgespanbasedonasetofgivenwindspec2traldensityfunctions.Uponobtainingwindve2locities,aerodynamicforcesactingonthebridge
girdercanbedeterminedbasedontheaerody2namicparametersobtainedbywindtunneltests.
Thepurposeofthepresentstudyistomodelthe
windfluctuationsalongtheTingKauBridge[5]
anddeterminetheaerodynamicforcesactingon
thebridgegirderaccordingtogivenwinddataand
aerodynamicparametersofthebridgedecksec2tion.
shownbyShinozukaandhisassociates[6,7]thata
setofmstationaryGaussianrandom
u0
i(t)(i=1,2,.,m)meansand
velocitytimehistorieshavetobesimulated,asis
oftenthecasefortheaerodynamicanalysisof
long-spanbridgesintimedomain.
Inviewoftheaboveproblem,anefficient
windfieldsimulationtechniqueforbridgesbased
ontheoriginalspectralrepresentationmethod
wasdevelopedbyYang[8]undercertainassump2tions.Considermwindvelocityprocesses,denot2edasui(t)(i=1,2,.,m),actingatmlocations
equallydistributedalongthespanwisedirectionof
cross-spectraldensityfunctionbe2turbulenceui(t)atlocationjand
82
JournalofSouthChinaUniversityofTechnology(NaturalScienceEdition)Vol.29
1
SimulationofWindFieldforLong-Span
Bridges
1.1 SimulationofWindTurbulencewithTempo2ral-SpatialCorrelations
Thespectralrepresentationmethodisthe
mostcommonlyusedmethodforsimulationof
multidimensionalrandomprocesseswithaspeci2fiedcross-spectraldensitymatrix.Ithasbeen
processes
one-
abridge.The
tweenwind
simulatedbythefollowingequations:
withzero
sidedtargetcross-spectraldensitymatrixScanbe
m
N
ui(t)=
2Δωcos[ωkt+
Σ∑
Hil(ωk)
l=1
k=1
θil(ωk)+φlk] (i=1,2,.,m)
(1)
where
Δω
=(ωmax-ωmin)/N
(2)
1
ωk=ωmin+(k-)Δω
2
Intheaboveequations,Nisthenumberoffre2quencyintervals;
ωmaxandωminaretheupperand
lowerfrequencylimits;
φlkistheindependent
randomphaseanglesuniformlydistributedbe2tween0and2π;
Hilisthe(i,l)entryofthelow2ertriangularmatrixHwhichisdeterminedby
Choleskydecompositionofthecross-spectralden2sitymatrixSasfollows:
S(ω)=H(ω)H.(ω)T(3)
inwhichthesuperbarindicatesthecomplexcon2jugateandthesuperscriptTdenotesthematrix
transposition.TheangleθilinEq.
(1)isthephase
angleofHildeterminedby
Im[Hil(ω)]
(4)
θil(ω)=tan-1
Re[Hil(ω)]
whereIm[·
]andRe[·
]representtheimaginary
andrealcomponentsofacomplexnumber,re2spectively.
Itcanbeseenfromtheabovederivationsthat
computationfortheconventionalspectralrepre2sentationmethodisverytime-consuming.Because
repetitivedecompositionofthecross-spectralden2sitymatrixSisneededifalargenumberofwind
uj(t)atlocationicanbedefinedas[2]
2nC2z(zj-zi)2+C2y(yj-yi)2
(5)
Sij=SiiSjjexp(-
Ui+Uj
whereSiiandSjjaretheauto-spectraldensity
functionsforprocessesui(t)anduj(t),respec2tively;
UiandUjarethemeanwindvelocitiesat
locationsiandj,respectively;
(yi,zi)and(yj,
zj)arethecoordinatesoflocationsiandj,re2
spectively;
nisthefrequencyinHertz;
CyandCz
aretheexponentialdecaycoefficients.
Assumethat(i)thebridgedeckisatthe
sameelevation,i.e.,zi=zj;
(ii)thewindfield
ishomogeneousalongthebridgespan,i.e.,Ui=
UjandSii=Sjj,and(iii)thelocationsonwhich
thewindvelocityprocessesactareequallydis2tributedalongthespanwisedirectionofthe
bridge,thenEq.(5)canberewrittenas
Sij=S11(cosα)j-i (j≥i)
(6)
inwhich
y2-y1
nCy
(7)
cosα=exp
-
U1
AccordingtoEq.(6),therealcross-spectralden2sitymatrixoftheprocessescanbewrittenas
1
sym.
cosα
S=S11(cosα)2cosα
…
w
(cosα)m-1(cosα)m-2(cosα)m-3.
(8)
AlowertriangularmatrixHthatsatisfiesEq.(3)
canbeexplicitlyderivedas[8]
No.10
SuChengetal:
ComputationofAerodynamicForcesforLong-SpanBridges 83
sinα
0
H=S11
(cosα)2sinαcosα
sinα
……
(cosα)m-1sinα(cosα)m-2sinα(cosα)m-3.sinα
(9)
SubstitutionofEq.(9)intoEq.
(1)yields
Ni
ui(t)=Σk=1Σl=1
Ailkcos(ωkt+φlk)
(i=1,2,.,m)(10)
where
andwarethecorrespondingfluctuatingcompo2nents.Inpracticalengineeringapplication,the
windturbulence(u,v,w)canbeconsideredas
stationaryGaussianrandomprocesseswithzero
meansandcanthereforebesimulatedbyusingthe
techniquesstatedinSection1.1.Sincetheeffect
oftheacross-windturbulencev(t)onbuffeting
forcesisusuallyneglected[2],onlythealong-wind
turbulenceu(t)andtheverticalturbulencew(t)are
neededtobegeneratedinthepresentsimulation.
Tocarryoutanumericalgenerationofwind
fluctuations,oneshouldchoosethewindspectra
Ailk=
(11)
al=1(
2ΔωS11(ωk)al(cosα)i-l=1),al=sinα(ll>
1)
ItisevidentthatEq.(10)requireslesscom2putationaleffortwhencomparedwiththeoriginal
spectralrepresentationmethodbyEqs.
(1)~
(4),
sincenoCholeskydecompositionisneededinthe
currentapproach.
1.2 SimulationofWindVelocityFieldforThe
TingKauBridge
RefertoarectangularCartesiancoordinates
(x,y,z)withyinspanwisedirection,xinhori2zontaldirectionnormaltoyandzinverticaldi2rection,respectively,asillustratedinFig.1.Let
thealong-winddirectionbeinahorizontalplane
andperpendiculartothebridgespan.Thenthe
componentsofthewindvelocityfieldalongthe
bridgedeckcanbeexpressedasfollows:
U(y,z,t)=Um(z)+u(y,z,t)
V(y,z,t)=v(y,z,t)
(12)
W(y,z,t)=w(y,z,t)
Fig.1 Cartesiancoordinatesandwindvelocitycomponents
whereU,V,andWarethewin
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- Computation of Aerodynamic Forces for LongSpan Bridges
链接地址:https://www.bdocx.com/doc/21058092.html