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球壳结构风压相关性研究

JournalofSoutheastUniversity(EnglishEdition)V01.26,No.1,PP.100—106Mar.2010ISSN1003—_7985Coherenceofwindpressureondomes

NyiNyiAungYeJihong

(KeyLaboratoryofConcreteandPrestressedConcreteStructureofMinistryofEducation,SoutheastUniversity,Nanjing210096,China)

Abstract:Theconceptofthecoherencefunctionisadoptedtofindthewindpressurecorrelationoftwopointsondomesofdifferentrise.spanratios.Thepressuremeasurementsaremadeonthe

domeroofmodelsbythewindtunneltest.Thecoherencefunctionsfordifferentseparationdistancesatseveraldirectionsofthedomesfromdifferentwinddirectionsareexamined.Theresultsshowthatthereisastrongcorrelationfortwoadjacentpointsatlowfrequency.butnotfornon.adjacentpoints.Thecoherenceofthewindpressureincreaseswiththedecreaseintheseparationdistance.Moreover,thecoherenceofthewindpressureisinthestrongestcorrelationonthealong—wind

directionatthesameseparation.butthelowestcorrelationisonthecross-winddirection.Thedetaileddeftvationoftheproposedexponentialcoherencemodelofthewindpressurefromexperimentaldataisalsodiscussed.Itisfoundthattheproposedexponentialcoherence

modelcanbeappropriate。especially,forsmallseparationsandthechangeinthedirectionsondomes.Basedonthequasi—steadytheory,therelationshipbetweenthewindpressureandthewindvelocityonthebasisofthecoherencemodelisalsoexamined.Thecoherenceobservedbetweenthewindpressureandthewindvelocityisnotadequatelypredictedbythequasi—steadytIleory.

Keywords:domes;coherenceofwindpressure;exponenfialcoherencemodelofwindpressure;quasi—steadYtheory

providealleasyandeconomicmethodoflarge

oftheroofandtheyarefrequentlyusedbythedesignerswhorealizetheadvantagesand

theelegantbeautyoftheconstruction….Sincethewindpressuresondomesvaryspatiallyasweilasintime.thedesignwindlpadsshouldbedeterminedbyconsideringthedynamiccharacter.isticsofwindpressures21.Long.spanandlightweightroofs.suchassphericalpneumaticdomes.tendtovibrateinstrongwinds。“.Inotherwords.windlpadshaveasignifi—cantproportionofthetotallpadactingonsuchstructuresand,sothemagnitudeanddistributionoftheresultantpres—suresmustbeconsidered041.Ogawaeta1.131experimentallyinvestigatedthetime.spacecorrelationofthewindpressuresinawindtunnelandconstructedasimplemodelofthepres-surefield.Hon901”“carriedoutaseriesofwind。tunnelex—perimentsonthemeanandfluctuatingwindpressuresbyin-vestigatingtheeffectsontheturbulenceoftheapproachingflowandthegeometryofdomesonthecharacteristicsofthepressurefield.Manyresearcheshavebeenfocusedonthecoherenceofthewindpressureonthesphericaldomes.Mo—Received2009旬8彤.

Biographies:NyiNyiAung(19r78一),male,gradual;YeJihong(eolTe-spondingauthor),female,doctor,professor.yejihong(W.Cell.edu.cn.

Foundationitem:TheNationalNaturalScienceFoundationofChinafNo.50678036).

Citation:NyiNyiAung,YeJihong.Coherenceofwindpressureondomes【J】.JoumalofSoutheastUniversity(EnglishEdition)。2010,26(1):100—106.reover,manywindloadingstandardsemployaquasi-steadyapproach

forthedesignofstructures.Unfortunately,manystudiesconcludethatthequasi—steadytheorycannotproperlypredictthecoherenceofthewindpressureandthecoherence

ofthewindvelocityl8吲.

1FittingMethodofCoherenceFunctionofWindPressure

Amathematicaldefinitionofthemagnitude??!;quaredco?-herencefunction,’,:(力,oftwostationaryrandomproces—

ses,iandJ,canbegivenas

y;(力=嘶Is,M)12(1)

whereS_i‘nands{tDaretheauto—sidedpowerspectraldensityfunctionofiandJ,respectively,atfrequency正Sij(Distheone—sidedcomplex—valuedcross—powerspectraldensityfunctionbetweenthetwoprocesses.Thecoherence7:(力isalwaysgreaterthanorequaltozeroandlessthanorequaltoone.

1.1Numericalstudies

Inthissection.thefrequencyofinterest.theinfluenceofseparationdistancesandtheinfluenceofdirectionarestud.iedtoestimategoodcoherencespectra.Toachievegoodes—timatesofcoherencespectra.itisnecessarytodefinetheappropriatetestingpointsandchoose

an印propnatepatroftestingpointson

structures.Basedonthewindtunnelpres—suretest,wecansymmetricallyobtainthewindpressuretime.historytestingpointsofthewholesurfaceofdomesasshowninFig.1.Thecoherencefunctionofdifkrentsepara-tionsofthedome(f:f=1:2)isbrieflystudiedalong00,300.600.90。directionsandsoon.But,forthedome(,:1=1:5),thecoherencefunctionisonlystudiedalong00。450.一45。and90。directions。becausethesuitablepairsoftestingpointsondomescanbeobtainedalongthesedi—rections(seeFig.1).

1.2Smoothtechnique

Itmustbenoticedthattheexperimentaldatashouldnotbefittedaftersmoothing,becausetheactofsmoothingin—validatestheassumptionthattheerrorsarenormallydistrib-uted….AdatasmoothingofthecoherencecurveiScarriedoutintIlispaperinordertostudytheinfluenceofbothfre—quencyandseparationdistancetoobtainthecoherencefuno-tion.Fig.2andFig.3showthecoherencefunctionsforad-iacentpointsandnon.adjacentpointsonallthedirectionsofdomes.Moreover,coherencefunctionsareclearlydepend—entontheseparationdistancesandtheanglesofdirection,asshowninTab.1.

102

NyiNyiAung,andYeJihong

Tab.1

Valuesofcoherencefunctionofdifferentseparationsof00

direction

on

domes

f-1=l:2,:1=I:5

坠!!!!塑!!堡

竺竺

!!!!堡!堡!!!堡!型

墨!竺唑

坠堡!!鬯!竺

型竺!!!!矍!!塑!!堡!!!

垦!翌唑

19I一179

13.048770.742

44

192.1826.890142

0.889

53

191.170

19】-164

191.158

191.15519l—l

25.8726835.22659

44.206ll

52.78802

60.855460.490

82

0.345

02

0.27923O.19582O.018

14

Right—side

ofdome

(windward)

192.172

192.164

192.158

192.154

192一152

13.7647220.6081927.405

ll

34.140

ll40.79798

0.784040.624580.493

67

0.384

590.29298Right-side

ofdome

(windward)

192.1

47.363680.00759

一~

191-5368.33736

0.025

03192-5253.82237

0.0174919l-56

191.62

19I一68191.77191.89

75.263

29

81.2632886.5825892.372

13

96.582500.024

14

0.02290

O.02l

23

0.02595

0.02375

Left—side

ofdome

(1eeward)

192-54

192_58192埘

192-72

192-82

60.159

46

66.36064

72.4ll

89

78.2995484.0lO29O.01656

0.01466O.Oll

57

0.014130.01409

Left—side

ofdome

(1eeward)

289192-9.53l26

O.018

73

Tab.1

givesthecharacteristicsofthecoherencefunction

ofdifferentseparationsof00directionondomes.Onthe

windwardportion。thelargestvaluesofcoherencefunctionsdecreasewiththeincreaseinseparationdistances.Ontheother

hand.allthelargestvaluesofcoherencefunctionson

theleewardportionarenearlyconstantandapproachzero.

Therefore.itcanbeconcludedthat

coherencesclearlyshow

the

relationship

between

the

separationdistancesoftwo

pointsandthecoherencefunction.

Thevaluesofthecoherencefunctionforallthedirections

are

showninTab.2.Itisfoundthatthevalueofthecoher-

ence

functionof00directionisthelargestforalltheangles

ofdirectionsf0。directionisalsocalledthewinddirec.

tion),butthesmallestvalueisinthe90。direction.Andthen,differentvaluesofthecoherencefunction

at(30。,

一30o)ale

bitlarge,buttheyarenearlyequalat(450,

一45。)and(60。,一60。)。Therelore,itcanbeseenthatit

obeysthesymmetryofdirectionsanddifferent

separation

distances.

Tab.2

Valuesofcoherencefunctionofallthedirections

on

domes

,:I=l:2

,:I=1:5

Angle

from

Pair

of

,,

Coherence

Angle

f如mPairof.,

winddirection

points∥m

(1argest)

winddirection

points

∥m

Coherence

(1argest)

0.889530.737

96

0.7762l

0.36937

型:

!竺:!垄!i:!坐!!Q:!塑竺

1.3

Derivationofproposedcoherencemodelofwindpressure

Thereisverylittleliteraturewindpressure.Someempiricalonthecoherencemodelofmodelsofwindvelocityfailtoaccountforreductionincoherenceatlowfrequenciesandlarge,separations…1“.Toaccountforsuchlimitations.inthissection,anexponentialcoherencemodelisproposed

anditisalso

empiricallybased.Usingtheleast.squarefit.

tingmethod,thetwo.termexponentialmodel,v=ae“+ce“,givesabetterstatisticaJfitthanothermodelsl131.Inthis

model,frequencyofimerest..separationdistancesandangleofdirectionmightbeemphasized,whichallowsfor

reductionin

coherence

withtheincreaseinseparationand

the

changeintheanglesofdirection.Thisexponentialco.

herence

modelcanbe

expressed

as

7;∽%缈={砌cos(詈)exp(bf)I/4+如cos(詈)expc扔∽)2

(2)

where

is

denoted

by(D—L“)/D

and

L“=

√【(工,一工f)2+(Yj—yf)2+(z,一zf)2】.Here,L玎is

the

separationdistanceoftwotestingpoints

at

pointsfand_『;

(xi,Yf,zf)and(J,,Y/,z,)arecoordinatesatpointsfandlj{isfrequencyofinterest;0istheangleofthedirectionfromthewinddirection;andDisthespanofthedome.Parametersa.b,canddcanbeestimatedfromestimatesofcoherencespectrabyonlyusingtheexperimentaldataofthedome(f:f=l:2).Inthenextsection,thenewcoher-

ence

model

can

becomparedwiththecoherencespe:ctraof

thedome(f:,=l:5).Hereinafter,itisshownthattheseparameterscannotbeestimatedfromsmoothingcoherencespectra.Forillustrationpurposes.datafromallthedirec-

tions

and

separation

distances

betweentesting

points

ale

used.Totally

300pairsofpointsareconsideredinthisre—

search.Toemployallofthedataandestimatetheparame-tersa,b.canddisofgreaterinterest.Theparametersa

and

cale

mostlygreaterthan

or

equaIto

zero

andalways

less

than

unity.But.thedecayparametersbandd

are

mostlylesstIlan

or

equal

tozero

andalwaysnegative.

MHMM

0OO

瓤眦跏捌E&&&

&j拍盯弛昵∞盯铊妒秽妒咿

“钙如谚∞

2288

3弭:g铊镐钙nnnn

"""丌"88

8∞∞∞∞∞n

n限‰n为弘踞抡盯叭∞%钙叭

旷妒妒科科

Coherenceofwindpressureondomes105

Fi孚7Comparisonofcoherencemodelsofwindpressureandwindvelocityusingdifferentseparationsofdome(,:l=1:2)(a)L=13.04877m;(b)L=25.87269m;(c)L=35.22659m

(b)(c)Fig.8Comparisonofcoherencemodelsofwindpressureandwindvelocityusingdifferentseparationsofdome(,:l=1:5).(a)L=13.76472m:(b)L=20.60819m;(c)L=27.4051m

tionforanytwopoints.Thecoherenceofthewindpressure

increaseswiththedecreaseintheseparationdistance.At

thesameseparationdistance,thecoherenceofthewind

pressureonthealong.winddirectionisinthestrongestCOl'-

relation,whilethecoherenceatthediagonalwinddirection

isinconsiderablystrongcorrelation.But.thecoherenceat

theacross.winddirectionisinthelowestcorrelation.

21Basedonthewindpressuretime.historyexperimental

data(totally300pairsofpoints)ofthedomewitharise-

spanratio(,:f=l:2),acoherencefunctionexpressionis

fittedbytheleast..squaresmethodtoobtainaproposedco..

herencemodel.andcomparedwiththeexperimentaldataof

domeswithrise—spanratios(f:f=l:2)and(f:f=l:5).

Theresultsshowthevalidestimatesofthecoherencespec—

trawiththeproposedcoherencemodel.But,thecoherence

functionoftheproposedmodellosesvalidestimatesat

largeseparationandlowfrequency.

31Intheprocessofcomparingthecoherenceofthepro-

posedmodelofthewindpressurewiththeexponentialco.

herenceofthewindvelocitydefinedbyDavenport.itis

foundthatthe

quasi??steadytheoryalsocannotproperlypre--

dictthecoherenceofthewindpressureondomes.

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球壳结构风压相关性研究

作者:尼尼昂, 叶继红, Nyi Nyi Aung, Ye Jihong

作者单位:东南大学混凝土与预应力混凝土结构教育部重点实验室,南京,210096

刊名:

东南大学学报(英文版)

英文刊名:JOURNAL OF SOUTHEAST UNIVERSITY(ENGLISH EDITION)

年,卷(期):2010,26(1)

被引用次数:1次

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