Q/SZJ191001-2017振動噪聲中隨機(jī)激勵分析規(guī)范RandomAnalysisforNoiseandVibration20XX20XX-12-31實(shí)施20XX-11-27發(fā)布XXXX汽車工程技術(shù)有限公司發(fā)布Q/SZXX-X-2017振動噪聲中隨機(jī)激勵分析規(guī)范范圍本標(biāo)準(zhǔn)規(guī)定了術(shù)語和定義、隨機(jī)激勵的定義、理論基礎(chǔ)等方面內(nèi)容。本標(biāo)準(zhǔn)適用于CAE部門NVH領(lǐng)域隨機(jī)激勵方面內(nèi)容。規(guī)范性引用文件無。術(shù)語和定義本規(guī)范涉及到的術(shù)語及其定義如下：NVHVibrationNoiseandharshness；PSD功率譜密度函數(shù)。摘要在振動和噪聲的解析工作中有兩種典型的載荷。第一種為確定類型的載荷，這種載荷為系統(tǒng)的，周期性的一般來說是可預(yù)測的力；第二種為隨機(jī)載荷，隨機(jī)載荷有很多種形式。本規(guī)范指的均為隨機(jī)載荷一種形式，這種載荷被認(rèn)為是平穩(wěn)遍歷類型。對于一種平穩(wěn)遍歷的力加載函數(shù)，線性并且時不變系統(tǒng)有以下關(guān)系：Therearebasicallytwotypesofloadingconditionstypicallyencounteredinnoiseandvibrationwork.Thefirstisadeterministictypeofload.Theseloadsaredotosystematic,periodic,andgenerallypredictableforces.Thesecondtypeistherandomload.Randomloadscantakemanyforms.Thisprocedurewillfocusonrandomloadsonly.Forthisprocedure,theloadswillbeconsideredtobestationaryandergodic.Forastationaryandergodicforcingfunction,theresponseofalinear,time-invariantsystemisasfollows:[Sxx]=[H][Sff][H]*式中[Sxx]定義為某自由度方向響應(yīng)的功率譜密度矩陣，[Sff]定義為系統(tǒng)輸入載荷的功率譜密度矩陣，[H]為從激勵點(diǎn)到響應(yīng)點(diǎn)的頻響函數(shù)矩陣，式中的“*”代表復(fù)數(shù)域內(nèi)的共軛轉(zhuǎn)置。With[Sxx]beingdefinedasthepowerspectraldensitymatrixoftheresponsedegreesoffreedom,[Sff]thepowerspectraldensitymatrixoftheinputloadstothesystem,[H]thematrixoffrequencyresponsefunctionsfromthepointsofinputapplicationtotheresponsepoints,and“*”designatingcomplexconjugatetranspose.典型工況中，上式中的功率譜密度矩陣均為全矩陣。這表明它們不但包含自功率譜，也包含互功率譜。互功率譜決定了不同輸入或者不同響應(yīng)之間的相位關(guān)系。假設(shè)互功率譜為0，表明系統(tǒng)的輸入之間是不相關(guān)的。Ingeneral,thetwopowerspectraldensitymatrices(PSD’s)arefullmatrices.Thisimpliesthattheynotonlycontaintheauto-PSD’s,butthecross-PSD’s.ItisthesecrossPSD’sthatdefinethephaserelationshipbetweendifferentinputs,ordifferentresponses.IncasethecrossPSD’sarezero,theinputstothesystemaretotallyuncorrelated.流程圖圖2.1流程圖Figure2.1ProcessFlowDiagram根據(jù)以上公式，很容易知道隨機(jī)分析需要分作兩步進(jìn)行。第一步即求解頻響函數(shù)矩陣，第二部為利用的功率譜密度矩陣激勵求解響應(yīng)。這些均可以由軟件MSC.Nastran來完成。該過程的第一個階段即求解頻響函數(shù)矩陣，然后，利用NASTRAN進(jìn)行后處理得到響應(yīng)的功率譜密度矩陣。Fromtheaboveequation,itcanreadilybeseenthattheprocessofarandomresponsecanbebrokenintotwoseparatesteps.SteponeistodeterminetheFRFmatricies.SteptwoistoapplytheinputPSD’stothesematricestoobtaintheresponse.This,infact,ishowMSC.NASTRANdoesitswork.ThefirstphaseoftheprocessistodeveloptheFRFmatrix.ThenNASTRAN,asapostprocessingactivity,appliesthatinformationtotheinputPSDmatrix.流程的第一步，求解頻響矩陣需要提前進(jìn)行。確切的說直接使用求解器SOL111或者SOL108即可。如果使用模態(tài)法求解頻響函數(shù)，需要考慮殘余向量。Thefirstpartoftheprocess,thedeterminationoftheFRFmatrices,isverystraightforward.ItisexactlylikearegularFRFrunusingSOL111,orSOL108.Eitherthemodalordirectsolutionsequencewillwork.However,ifusingthemodalsolutionsequence,caremustbetakenrelativetoresidualvectorissues.(SeeFRFprocedurefordetails.)工具描述仿真分析過程中需要用到的如下軟件:Thefollowingsoftwarefacilitatestheanalyticalsimulationprocess:前處理(Preprocessors):Hypermesh求解器(AnalysisCode):MSC.Nastran后處理(Postprocessors):Hyperview建模和分析過程N(yùn)/A假設(shè)和限制假設(shè)Assumptions在隨機(jī)分析中有三個基本假設(shè)。第一個就是系統(tǒng)是線性和時不變的。其他的兩個是激勵信號具有平穩(wěn)遍歷的特點(diǎn)。平穩(wěn)意味著激勵大小的概率分布隨著時間的推進(jìn)不會改變。舉個例子：假設(shè)載荷加載了10分鐘，載荷大小的平均值在第一分鐘內(nèi)和在10分鐘內(nèi)是一樣的。遍歷性指不管是取一個樣本還是取多個樣本，信號的平均值是相同的，例如有10組數(shù)據(jù)，其平均值同其中任何一組數(shù)據(jù)的平均值都是相同的。Therearethreebasicassumptionsusedinthismethodofmodelingrandomresponses.Thefirstisthatthesystemislinearandtime-invariant.Theothertwoarethattheinputsarestationaryandergodic.Stationarymeansthattheprobabilitydistributionsoftheinputsdonotchangeovertime;i.e.iftheloadweretobeappliedfortenminutes,theaverageoftheinputloadinthefirstminuteisthesameastheaverageoftheloadinthetenthminute.Ergodicityreferstoadifferentkindofinvariance.Itimpliesthattheaverageofthesignalisthesameacrosstheensembleofdataasitisforonesampleovertime.So,iftherewheretengroupsofdata,theaverageoverthegroupatagiventimewouldbeexactlythesameastheaverageoveroneofthetenforalltime.Bothoftheseassumptionstendtobegoodassumptionsinthenoiseandvibrationdiscipline.限制LimitationsN/A載荷和邊界條件邊界條件N/A載荷假設(shè)一個系統(tǒng)有三個載荷和三個響應(yīng)點(diǎn)，NASTRAN的計(jì)算文件將如下進(jìn)行設(shè)置：Forthepurposesofillustration,assumethereisasystemwiththreeloadsapplied,andthreeresponsepoints.TheNASTRANdeckwouldbesetupasfollows:三個激勵點(diǎn)的編號分別為1001,1002和1003，三個響應(yīng)點(diǎn)的編號分別為9001,9002和9003。Nasrtan的計(jì)算文件是以頻響計(jì)算文件為基礎(chǔ)，所以執(zhí)行控制部分應(yīng)該有：Thethreeinputpointsaregrids1001,1002and1003.Thethreeresponsepointsaregrids9001,9002,and9003.ThedeckisabasicFRFdeckwithaSOL108,orSOL111,sotheexecutivecontrolsectionwouldhave:SOL111(or108)CENDThecasecontrol部分有提取頻率段的FREQUENCY卡片：ThecasecontrolmustalsohaveaFREQUENCYcardreferringtothefrequenciesofinterest.FREQUENCY=100提取模態(tài)值的METHOD卡片。TheremustalsobeaMETHODcardifthisisamodalsolution.METHOD=200隨機(jī)分析的計(jì)算文件與頻響分析的不同點(diǎn)就是RANDOM卡片的必須的。該卡片應(yīng)該放置在所有的SUBCASE后，RANDOM卡片引用的是在BULKDATA數(shù)據(jù)中的RANDPS卡片。ThefirstdifferencetoanormalSOL111(108)runistheRANDOMcardthatisneeded.ItshouldbeplaceaboveallfollowingSUBCASElines.TheIDreferencedbytheRANDOMcardwillcalltheRANDPScardintheBULKDATAsection(explanationwillfollow)假設(shè)一個系統(tǒng)有三個載荷和三個響應(yīng)點(diǎn)，NASTRAN的計(jì)算文件將如下進(jìn)行設(shè)置：Forthepurposesofillustration,assumethereisasystemwiththreeloadsapplied,andthreeresponsepoints.TheNASTRANdeckwouldbesetupasfollows:三個激勵點(diǎn)的編號分別為1001,1002和1003，三個響應(yīng)點(diǎn)的編號分別為9001,9002和9003。Nasrtan的計(jì)算文件是以頻響計(jì)算文件為基礎(chǔ)，所以執(zhí)行控制部分應(yīng)該有：Thethreeinputpointsaregrids1001,1002and1003.Thethreeresponsepointsaregrids9001,9002,and9003.ThedeckisabasicFRFdeckwithaSOL108,orSOL111,sotheexecutivecontrolsectionwouldhave:SOL111(or108)CENDThecasecontrol部分有提取頻率段的FREQUENCY卡片：ThecasecontrolmustalsohaveaFREQUENCYcardreferringtothefrequenciesofinterest.FREQUENCY=100提取模態(tài)值的METHOD卡片。TheremustalsobeaMETHODcardifthisisamodalsolution.METHOD=200隨機(jī)分析的計(jì)算文件與頻響分析的不同點(diǎn)就是RANDOM卡片的必須的。該卡片應(yīng)該放置在所有的SUBCASE后，RANDOM卡片引用的是在BULKDATA數(shù)據(jù)中的RANDPS卡片。ThefirstdifferencetoanormalSOL111(108)runistheRANDOMcardthatisneeded.ItshouldbeplaceaboveallfollowingSUBCASElines.TheIDreferencedbytheRANDOMcardwillcalltheRANDPScardintheBULKDATAsection(explanationwillfollow)RANDOM=3000計(jì)算頭文件應(yīng)該包含兩部分的功能。一個為從激勵點(diǎn)到響應(yīng)點(diǎn)的頻響傳涵矩陣[H]的產(chǎn)生，一個為輸入的功率譜密度矩陣[Sff]的產(chǎn)生，下面分別描述兩個矩陣的產(chǎn)生過程：AsstatedinParagraph1.2theloadingofthesystemdoesconsistoftwoparts:thegenerationofthe[H]-matrixthatcontainstheFRFsfromtheloadingtotheoutputDOFs;thedefinitionoftheinputPSD’matrix[Sff].a）頻響傳涵矩陣[H]的產(chǎn)生a)Generationofthe[H]-matrix頻響函數(shù)矩陣的產(chǎn)生的卡片設(shè)置方法同規(guī)范《HarmonicFrequencyResponseAnalysis》。FRF’sgenerationcanrefertotheprocedure<HarmonicFrequencyResponseAnalysis>.b）激勵信號的功率譜密度矩陣[Sff]的產(chǎn)生b)GenerationoftheinputPSDmatrix[Sff]流程的下一步就是設(shè)置激勵的功率譜密度矩陣?？刂瓶ㄆ琑ANDOM會指定功率譜密度矩陣，該矩陣可以用卡片RANDPS來存儲。功率譜密度是一種頻域內(nèi)的復(fù)雜的數(shù)據(jù)，其實(shí)部和虛部均需要定義，實(shí)際上，PSD數(shù)據(jù)被保存在TABRND1卡片中，RANDPS卡片直接引用TABLED1卡片的數(shù)據(jù)即可。ThenextstepoftheprocessistosetuptheinputPSDmatrix[Sff].ThecasecontrolRANDOMcardpointstothedesignatedPSDmatrix.ThematrixisputinwiththeRANDPScards.ThePSDsarecomplexdataoverfrequency.So,realandimaginarypartofeachentryhastobedefined.TheactualPSDdataoverfrequencyisheldintables(TABRND1-Table).TheRANDPScardsdotellNASTRANwhichtabledoescontaindataforwhichentryinthematrix[Sff].組裝的RANDPS卡片直接被RANDOM調(diào)用。TheRANDPScardssecondfieldisjustthenumberdesignatedontheRANDOMcasecontrolcommand.ItisthesameforalltheRANDPScards.接下來進(jìn)行載荷矩陣的調(diào)整（PSD矩陣的行列是對稱的，所有只需要關(guān)注上三角矩陣即可）。PSD矩陣的元素分別由計(jì)算步長來指定，并且矩陣的第一個元素一定有在計(jì)算中使用。Thenexttwofieldsdesignatethematrixcoordinatesoftheloaddatabeingspecified(rowandcolumn--PSDmatricesarehermetian,therefore,onlytheuppertriangleisneeded).AstheSUBCASEIDisanarbitrarynumbertheSUBCASEIDitself(here15,25,35)mustberelatedtotherowandcolumninthePSDmatrix.Toreferencethecolumn1orrow1inthePSDmatrixthefirstSUBCASE(hereID15)hastobeused.RANDPS卡片中的實(shí)值和虛值會有放大系數(shù)設(shè)置選項(xiàng)。一般來說，實(shí)部虛部兩個放大系數(shù)中只有一個是非零的。對于互功率譜工況，有典型的兩種情況，一個是實(shí)部為零，一種為虛部為零。在這里強(qiáng)烈建議不要使用任何不為1的放大系數(shù)，除非是單位的轉(zhuǎn)換需要。Thenexttwofieldsarethescalefactorsfortherealandimaginaryportionofthedata.Normally,onlyoneofthesefieldsisnon-zero.Forthecaseofacrossspectraldensityinput,therearetypicallytwolines;onewiththerealpartzero,andonewiththeimaginarypartzero.Itisstronglyrecommendednottouseanyscalingfactorexcepttodounitadjustment.Inthatway,thedataisdefinedinaselfconsistentmanner.最后功率譜密度矩陣被定義成表格的類型，由各RANDPS組裝的卡片為矩陣的每個元素，典型的RANDPS卡片的設(shè)置如下：ThelastfieldistheidentifierfortheTABRNDcardthatholdsthetabulardataforthePSD.So,typicalRANDPSinputlookslikethis:RANDPS,3000,15,15,1.0,0.0,3001RANDPS,3000,15,25,1.0,0.0,3002RANDPS,3000,15,25,0.0,1.0,3003RANDPS,3000,15,35,1.0,0.0,3004RANDPS,3000,15,35,0.0,1.0,3005RANDPS,3000,25,25,1.0,0.0,3006RANDPS,3000,25,35,1.0,0.0,3007RANDPS,3000,25,35,0.0,1.0,3008RANDPS,3000,35,35,1.0,0.0,3009圖7.1由RANDPS卡片設(shè)置的PSD矩陣示意圖fig.7.1illustrationhowthePSDinputmatrixissetupbytheRANDPScards語句“RANDPS,3000,15,15,1.0,0.0,3001”意味著分析步15被定義成自功率譜密度載荷，由于分析步15是計(jì)算文件中第一個分析步長，其RANDPS放置在自功率譜密度矩陣[Sff]的第一行第一列。Thismeanstheline“RANDPS,3000,15,15,1.0,0.0,3001”definestheautoPSDoftheloaddefinedinSUBCASE15.AsSUBCASE15isthefirstSUBCASEdefinedintheCASECONTROLsectionthislinedefinesrow1andcolumn1ofthePSDmatrix[Sff].語句“RANDPS,3000,25,35,1.0,0.0,3007”定義為分析步25和35的實(shí)部的互功率譜密度。語句“RANDPS,3000,25,35,0.0,1.0,3008”定義為分析步25和35的虛部互功率譜密度。由于步長25和35分別為計(jì)算文件的第二個和第三個步長，其傳涵也在FRF矩陣的第二行和第三行，所以前兩個語句的RANDPS均存儲在功率譜密度矩陣[Sff]的第三行、第二列。Theline“RANDPS,3000,25,35,1.0,0.0,3007”definestherealpartofthecrossPSDbetweenloaddefinedinSUBCASE25andSUBCASE35.Theline“RANDPS,3000,25,35,0.0,1.0,3008”definestheimaginarypartofthecrossPSDbetweenloaddefinedinSUBCASE25andSUBCASE35.AsSUBCASE25isthesecondSUBCASEandSUBCASE35isthethirdSUBCASEdefinedintheCASECONTROLsectiontheydefinethesecondandthirdcolumnsoftheFRFmatrix.Therefore,thisRANDPSlinedefinesrow2andcolumn3ofthePSDmatrix[Sff].As[Sff]ishermetianitsimultaneouslydefinesrow3/column2.頻域內(nèi)的功率譜密度數(shù)據(jù)可以存儲在TABRND卡片中，如下：ThePSDdataoverfrequencyisstoredinTABRNDtables:TABRND,3001+,1.0,3.5,2.0,4.2,3.0,5.5,4.0,1.3…+,ENDT在BULK數(shù)據(jù)中，在求解模態(tài)的計(jì)算步中，除了實(shí)際模型的約束，也包含EIGRL卡片。Thebulkdatadeck,besidescontainingtheactualmodel,willalsocontainandEIGRLcardifthisismodalsolution.性能要求N/A分析要求軟件Software仿真分析過程中用到的軟件為MSC.NASTRANThebasictoolusedisMSC.NASTRAN其他信息otherImformationN/A結(jié)果RESULTS要把功率譜密度信息寫入到*.pch文件中，首先要弄清楚應(yīng)該輸出什么。節(jié)點(diǎn)編號（或者單元編號）、自由度方向（激勵力的或者某單元的）和輸出的類型（位移、速度、加速度和力等）都是必須的。ThefirststeptogettingthePSDinformationintoapunchfileinvolvesunderstandingexactlywhatoutputisrequested.Thegridnumber(orelementnumber),thedirection(orforcecodeforanelement),andwhattypeofoutput(displacement,velocity,acceleration,force,etc.)areallneeded.輸出請求中首先就應(yīng)該包含頻響矩陣，然后也應(yīng)該包含功率譜密度矩陣。TheoutputhastoberequestedfirstfortheHmatrix,andthenfortheoutputPSD.Thesetwooutputrequestshavetobeconsistent.使用SOL111或者SOL108求解器輸出頻響矩陣[H]，可以為位移、速度、加速度或者力相關(guān)的輸出量，結(jié)果簡單的寫入到PLOT中而不必設(shè)置卡片PARAM,POST,-1or-2（應(yīng)該op2數(shù)據(jù)不會運(yùn)用到也浪費(fèi)求解時間）。TheHmatrixoutputgetsrequestedasitisdoneforanormalSOL111orSO