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
a
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
h
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
O
瓤眦跏捌E&&&
&j拍盯弛昵∞盯铊妒秽妒咿
一
“钙如谚∞
2288
3弭:g铊镐钙nnnn
n
"""丌"88
8
8
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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