振动噪声随机激励分析规范

Q/SZJ191001-2017振动噪声中随机激励分析规范RandomAnalysisforNoiseandVibration20XX20XX-12-31实施20XX-11-27发布XXXX汽车工程技术有限公司发布Q/SZXX-X-2017振动噪声中随机激励分析规范范围本标准规定了术语和定义、随机激励的定义、理论基础等方面内容。本标准适用于CAE部门NVH领域随机激励方面内容。规范性引用文件无。术语和定义本规范涉及到的术语及其定义如下：NVHVibrationNoiseandharshness；PSD功率谱密度函数。摘要在振动和噪声的解析工作中有两种典型的载荷。第一种为确定类型的载荷，这种载荷为系统的，周期性的一般来说是可预测的力；第二种为随机载荷，随机载荷有很多种形式。本规范指的均为随机载荷一种形式，这种载荷被认为是平稳遍历类型。对于一种平稳遍历的力加载函数，线性并且时不变系统有以下关系：Therearebasicallytwotypesofloadingconditionstypicallyencounteredinnoiseandvibrationwork.Thefirstisadeterministictypeofload.Theseloadsaredotosystematic,periodic,andgenerallypredictableforces.Thesecondtypeistherandomload.Randomloadscantakemanyforms.Thisprocedurewillfocusonrandomloadsonly.Forthisprocedure,theloadswillbeconsideredtobestationaryandergodic.Forastationaryandergodicforcingfunction,theresponseofalinear,time-invariantsystemisasfollows:[Sxx]=[H][Sff][H]*式中[Sxx]定义为某自由度方向响应的功率谱密度矩阵，[Sff]定义为系统输入载荷的功率谱密度矩阵，[H]为从激励点到响应点的频响函数矩阵，式中的“*”代表复数域内的共轭转置。With[Sxx]beingdefinedasthepowerspectraldensitymatrixoftheresponsedegreesoffreedom,[Sff]thepowerspectraldensitymatrixoftheinputloadstothesystem,[H]thematrixoffrequencyresponsefunctionsfromthepointsofinputapplicationtotheresponsepoints,and“*”designatingcomplexconjugatetranspose.典型工况中，上式中的功率谱密度矩阵均为全矩阵。这表明它们不但包含自功率谱，也包含互功率谱。互功率谱决定了不同输入或者不同响应之间的相位关系。假设互功率谱为0，表明系统的输入之间是不相关的。Ingeneral,thetwopowerspectraldensitymatrices(PSD’s)arefullmatrices.Thisimpliesthattheynotonlycontaintheauto-PSD’s,butthecross-PSD’s.ItisthesecrossPSD’sthatdefinethephaserelationshipbetweendifferentinputs,ordifferentresponses.IncasethecrossPSD’sarezero,theinputstothesystemaretotallyuncorrelated.流程图图2.1流程图Figure2.1ProcessFlowDiagram根据以上公式，很容易知道随机分析需要分作两步进行。第一步即求解频响函数矩阵，第二部为利用的功率谱密度矩阵激励求解响应。这些均可以由软件MSC.Nastran来完成。该过程的第一个阶段即求解频响函数矩阵，然后，利用NASTRAN进行后处理得到响应的功率谱密度矩阵。Fromtheaboveequation,itcanreadilybeseenthattheprocessofarandomresponsecanbebrokenintotwoseparatesteps.SteponeistodeterminetheFRFmatricies.SteptwoistoapplytheinputPSD’stothesematricestoobtaintheresponse.This,infact,ishowMSC.NASTRANdoesitswork.ThefirstphaseoftheprocessistodeveloptheFRFmatrix.ThenNASTRAN,asapostprocessingactivity,appliesthatinformationtotheinputPSDmatrix.流程的第一步，求解频响矩阵需要提前进行。确切的说直接使用求解器SOL111或者SOL108即可。如果使用模态法求解频响函数，需要考虑残余向量。Thefirstpartoftheprocess,thedeterminationoftheFRFmatrices,isverystraightforward.ItisexactlylikearegularFRFrunusingSOL111,orSOL108.Eitherthemodalordirectsolutionsequencewillwork.However,ifusingthemodalsolutionsequence,caremustbetakenrelativetoresidualvectorissues.(SeeFRFprocedurefordetails.)工具描述仿真分析过程中需要用到的如下软件:Thefollowingsoftwarefacilitatestheanalyticalsimulationprocess:前处理(Preprocessors):Hypermesh求解器(AnalysisCode):MSC.Nastran后处理(Postprocessors):Hyperview建模和分析过程N/A假设和限制假设Assumptions在随机分析中有三个基本假设。第一个就是系统是线性和时不变的。其他的两个是激励信号具有平稳遍历的特点。平稳意味着激励大小的概率分布随着时间的推进不会改变。举个例子：假设载荷加载了10分钟，载荷大小的平均值在第一分钟内和在10分钟内是一样的。遍历性指不管是取一个样本还是取多个样本，信号的平均值是相同的，例如有10组数据，其平均值同其中任何一组数据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载荷和边界条件边界条件N/A载荷假设一个系统有三个载荷和三个响应点，NASTRAN的计算文件将如下进行设置：Forthepurposesofillustration,assumethereisasystemwiththreeloadsapplied,andthreeresponsepoints.TheNASTRANdeckwouldbesetupasfollows:三个激励点的编号分别为1001,1002和1003，三个响应点的编号分别为9001,9002和9003。Nasrtan的计算文件是以频响计算文件为基础，所以执行控制部分应该有：Thethreeinputpointsaregrids1001,1002and1003.Thethreeresponsepointsaregrids9001,9002,and9003.ThedeckisabasicFRFdeckwithaSOL108,orSOL111,sotheexecutivecontrolsectionwouldhave:SOL111(or108)CENDThecasecontrol部分有提取频率段的FREQUENCY卡片：ThecasecontrolmustalsohaveaFREQUENCYcardreferringtothefrequenciesofinterest.FREQUENCY=100提取模态值的METHOD卡片。TheremustalsobeaMETHODcardifthisisamodalsolution.METHOD=200随机分析的计算文件与频响分析的不同点就是RANDOM卡片的必须的。该卡片应该放置在所有的SUBCASE后，RANDOM卡片引用的是在BULKDATA数据中的RANDPS卡片。ThefirstdifferencetoanormalSOL111(108)runistheRANDOMcardthatisneeded.ItshouldbeplaceaboveallfollowingSUBCASElines.TheIDreferencedbytheRANDOMcardwillcalltheRANDPScardintheBULKDATAsection(explanationwillfollow)假设一个系统有三个载荷和三个响应点，NASTRAN的计算文件将如下进行设置：Forthepurposesofillustration,assumethereisasystemwiththreeloadsapplied,andthreeresponsepoints.TheNASTRANdeckwouldbesetupasfollows:三个激励点的编号分别为1001,1002和1003，三个响应点的编号分别为9001,9002和9003。Nasrtan的计算文件是以频响计算文件为基础，所以执行控制部分应该有：Thethreeinputpointsaregrids1001,1002and1003.Thethreeresponsepointsaregrids9001,9002,and9003.ThedeckisabasicFRFdeckwithaSOL108,orSOL111,sotheexecutivecontrolsectionwouldhave:SOL111(or108)CENDThecasecontrol部分有提取频率段的FREQUENCY卡片：ThecasecontrolmustalsohaveaFREQUENCYcardreferringtothefrequenciesofinterest.FREQUENCY=100提取模态值的METHOD卡片。TheremustalsobeaMETHODcardifthisisamodalsolution.METHOD=200随机分析的计算文件与频响分析的不同点就是RANDOM卡片的必须的。该卡片应该放置在所有的SUBCASE后，RANDOM卡片引用的是在BULKDATA数据中的RANDPS卡片。ThefirstdifferencetoanormalSOL111(108)runistheRANDOMcardthatisneeded.ItshouldbeplaceaboveallfollowingSUBCASElines.TheIDreferencedbytheRANDOMcardwillcalltheRANDPScardintheBULKDATAsection(explanationwillfollow)RANDOM=3000计算头文件应该包含两部分的功能。一个为从激励点到响应点的频响传涵矩阵[H]的产生，一个为输入的功率谱密度矩阵[Sff]的产生，下面分别描述两个矩阵的产生过程：AsstatedinParagraph1.2theloadingofthesystemdoesconsistoftwoparts:thegenerationofthe[H]-matrixthatcontainstheFRFsfromtheloadingtotheoutputDOFs;thedefinitionoftheinputPSD’matrix[Sff].a）频响传涵矩阵[H]的产生a)Generationofthe[H]-matrix频响函数矩阵的产生的卡片设置方法同规范《HarmonicFrequencyResponseAnalysis》。FRF’sgenerationcanrefertotheprocedure<HarmonicFrequencyResponseAnalysis>.b）激励信号的功率谱密度矩阵[Sff]的产生b)GenerationoftheinputPSDmatrix[Sff]流程的下一步就是设置激励的功率谱密度矩阵。控制卡片RANDOM会指定功率谱密度矩阵，该矩阵可以用卡片RANDPS来存储。功率谱密度是一种频域内的复杂的数据，其实部和虚部均需要定义，实际上，PSD数据被保存在TABRND1卡片中，RANDPS卡片直接引用TABLED1卡片的数据即可。ThenextstepoftheprocessistosetuptheinputPSDmatrix[Sff].ThecasecontrolRANDOMcardpointstothedesignatedPSDmatrix.ThematrixisputinwiththeRANDPScards.ThePSDsarecomplexdataoverfrequency.So,realandimaginarypartofeachentryhastobedefined.TheactualPSDdataoverfrequencyisheldintables(TABRND1-Table).TheRANDPScardsdotellNASTRANwhichtabledoescontaindataforwhichentryinthematrix[Sff].组装的RANDPS卡片直接被RANDOM调用。TheRANDPScardssecondfieldisjustthenumberdesignatedontheRANDOMcasecontrolcommand.ItisthesameforalltheRANDPScards.接下来进行载荷矩阵的调整（PSD矩阵的行列是对称的，所有只需要关注上三角矩阵即可）。PSD矩阵的元素分别由计算步长来指定，并且矩阵的第一个元素一定有在计算中使用。Thenexttwofieldsdesignatethematrixcoordinatesoftheloaddatabeingspecified(rowandcolumn--PSDmatricesarehermetian,therefore,onlytheuppertriangleisneeded).AstheSUBCASEIDisanarbitrarynumbertheSUBCASEIDitself(here15,25,35)mustberelatedtotherowandcolumninthePSDmatrix.Toreferencethecolumn1orrow1inthePSDmatrixthefirstSUBCASE(hereID15)hastobeused.RANDPS卡片中的实值和虚值会有放大系数设置选项。一般来说，实部虚部两个放大系数中只有一个是非零的。对于互功率谱工况，有典型的两种情况，一个是实部为零，一种为虚部为零。在这里强烈建议不要使用任何不为1的放大系数，除非是单位的转换需要。Thenexttwofieldsarethescalefactorsfortherealandimaginaryportionofthedata.Normally,onlyoneofthesefieldsisnon-zero.Forthecaseofacrossspectraldensityinput,therearetypicallytwolines;onewiththerealpartzero,andonewiththeimaginarypartzero.Itisstronglyrecommendednottouseanyscalingfactorexcepttodounitadjustment.Inthatway,thedataisdefinedinaselfconsistentmanner.最后功率谱密度矩阵被定义成表格的类型，由各RANDPS组装的卡片为矩阵的每个元素，典型的RANDPS卡片的设置如下：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图7.1由RANDPS卡片设置的PSD矩阵示意图fig.7.1illustrationhowthePSDinputmatrixissetupbytheRANDPScards语句“RANDPS,3000,15,15,1.0,0.0,3001”意味着分析步15被定义成自功率谱密度载荷，由于分析步15是计算文件中第一个分析步长，其RANDPS放置在自功率谱密度矩阵[Sff]的第一行第一列。Thismeanstheline“RANDPS,3000,15,15,1.0,0.0,3001”definestheautoPSDoftheloaddefinedinSUBCASE15.AsSUBCASE15isthefirstSUBCASEdefinedintheCASECONTROLsectionthislinedefinesrow1andcolumn1ofthePSDmatrix[Sff].语句“RANDPS,3000,25,35,1.0,0.0,3007”定义为分析步25和35的实部的互功率谱密度。语句“RANDPS,3000,25,35,0.0,1.0,3008”定义为分析步25和35的虚部互功率谱密度。由于步长25和35分别为计算文件的第二个和第三个步长，其传涵也在FRF矩阵的第二行和第三行，所以前两个语句的RANDPS均存储在功率谱密度矩阵[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.频域内的功率谱密度数据可以存储在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数据中，在求解模态的计算步中，除了实际模型的约束，也包含EIGRL卡片。Thebulkdatadeck,besidescontainingtheactualmodel,willalsocontainandEIGRLcardifthisismodalsolution.性能要求N/A分析要求软件Software仿真分析过程中用到的软件为MSC.NASTRANThebasictoolusedisMSC.NASTRAN其他信息otherImformationN/A结果RESULTS要把功率谱密度信息写入到*.pch文件中，首先要弄清楚应该输出什么。节点编号（或者单元编号）、自由度方向（激励力的或者某单元的）和输出的类型（位移、速度、加速度和力等）都是必须的。ThefirststeptogettingthePSDinformationintoapunchfileinvolvesunderstandingexactlywhatoutputisrequested.Thegridnumber(orelementnumber),thedirection(orforcecodeforanelement),andwhattypeofoutput(displacement,velocity,acceleration,force,etc.)areallneeded.输出请求中首先就应该包含频响矩阵，然后也应该包含功率谱密度矩阵。TheoutputhastoberequestedfirstfortheHmatrix,andthenfortheoutputPSD.Thesetwooutputrequestshavetobeconsistent.使用SOL111或者SOL108求解器输出频响矩阵[H]，可以为位移、速度、加速度或者力相关的输出量，结果简单的写入到PLOT中而不必设置卡片PARAM,POST,-1or-2（应该op2数据不会运用到也浪费求解时间）。TheHmatrixoutputgetsrequestedasitisdoneforanormalSOL111orSO