OptiStruct随机振动分析

InnovationIntelligence®OptiStruct随机振动分析马越峰yuefeng.ma@altair.com.cnsupport@altair.com.cn(supportemail)4006-196-186(supporthotline)28-April-2014Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.2振动分类—按载荷形式和响应类型Classificationofvibration2线性系统LinearsystemDynamicresponse自由振动FreeVibration(f=0)强迫振动(外力、压强)EnforcedVibration(Force,Pressure)()MxCxKxft正则模态分析RealEigen/Modes复模态分析ComplexEigen/Modes强迫运动(加速度、位移)EnforcedMotion(Acceleration,Displacement)瞬态响应Transientresponse频率响应Frequencyresponse随机振动响应RandomResponse精确分析统计分析峰值分析响应谱等SRS,DDAMCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.强迫运动激励首先一定是固定在某些“基础”之上的。强迫振动？强迫运动激励？Lunchload地震波Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.定义节点1的位移时间历程的自动强迫运动HyperMesh中定义两个约束：‒SPCD定义节点1的强迫运动位移‒SPC定义节点约束•SPC必须约束住加载自由度•SPC是否需要约束其它自由度？强迫运动–虚拟约束法SPCDNode1ZdirectionCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.SPCD定义节点1的强迫运动量SPC定义节点1的约束，这是一个虚拟约束强迫运动–虚拟约束法SPCDNode1Zdirection对于SPCD方法，虚约束自由度同时又是运动加载自由度！Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.6()rut()gut()()grutut参考轴质点位移()()()rgututut质点加速度惯性力弹性恢复力阻尼力rrrgeffmucukumup运动方程()()()rgututut()()Irgfmutmut()srfkut()drfcut强迫运动的绝对响应和相对响应xglobal惯性系非惯性系质量M阻尼CCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.7ENFMOTN参数控制绝对位移和相对位移的输出PARAM,ENFMOTN,ABS‒ABS的缺省值表示分析结果是模型的绝对运动PARAM,ENFMOTN,REL‒假如值被定义为REL,那么运动相对于强迫运动的基础。在模态振动分析中，这等效于用大质量法和从分析中排除刚体运动。PARAM,ENFMOTNCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.8数据分类ClassificationofPhysicalDataRandomStationaryNon-StationaryNon-ErgodicDeterministicPhysicalDataRandomvibrationErgodic各态历经过程ShockSpectrumTransientReproducethedatabycontrolledexperiments可控性FrequencyCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.9StationaryandErgodic稳态数据和各态历经过程•Stationary:Foreveryt,PDF(ProbabilityDensityFunction),xandx2ofeveryrecordareconstant.对每个采样数据，概率密度函数，x和x2是恒定的。•Ergodic:Iftherandomprocessisstationary,andthecharactersofanysinglerecordarethesameastheensembleofrecords.对所有的采样数据，任意时间段内都是稳态的数据采样asample(realization,record)oftherandomprocessCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.10各态历经随机信号，N(µ,σ)ErgodicRandomsignal10211niiaRMSn工程上常见的随机信号，可以用高斯分布，即正态分布来表示。均方根( 标准 excel标准偏差excel标准偏差函数exl标准差函数国标检验抽样标准表免费下载红头文件格式标准下载 差Standarddeviation)：每个 样本 保单样本pdf木马病毒样本下载上虞风机样本下载直线导轨样本下载电脑病毒样本下载 点到平均值的平均距离。x，x只能反映载荷的幅值或者强度变化，但是完全不能反映频谱特性22()21()2xxFxedxTimeµacceaccePdf0Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.11正态分布的特征charactersofnormaldistribution11平均值的影响标准差的影响Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.12随机振动分析方法有两个基本假设：‒载荷和响应满足正态分布假设‒载荷和响应满足零平均值假设随机振动响应的两个基本假设12Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.13σP(|x|σ)P(|x|>σ)PerMillion/每百万1σ68.27%31.7%317,3002σ95.45%4.55%45,5002.5σ98.76%1.24%12,4003σ99.73%0.27%2,7003.5σ99.953%0.047%4704σ99.9937%0.0063%635σ99.999943%0.000057%0.576σ99.9999998%0.0000002%0.00212323145645σ699.73%安全区域危险区域0.135%危险区域0.135%22()21()2xxFxedx正态分布的置信水平1σ~3σ随机振动采用双边置信水平211niiRMSanCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.14随机振动结果的常用置信水平Commonconfidencelevelforrandomvibration142221()2xxFxedxσ安全率失效率2.5σ98.76%1.24%3σ99.73%3‰3.5σ99.953%0.047%随机振动结果通常使用3双边置信，即±3Timeµ=0-g+gacce3σaccePdf2σσCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.15PSD定义公式PSDFunctiondefinition1()()2ixxxxSRde自功率谱密度函数定义(Auto)PSD()()ixxxxRSdARMSAePSDf1f2A/2/21()lim()TxxtTRExtxtxtxtdtT2222(),()(0)xxxxxxxxxxRRR自相关函数：(Auto)correctionCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.16PSD计算公式PSDFunctionCalculation16双边谱1()()2ixxxxSRdePSD使用单边谱2000xxxxSG21()xxSFFTxtTCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.17如何生成PSD载荷ConverttimerecordstoPSD17PSD(g2)/Hzf1AInputPSD=Envelopecurve包络线f2不同路面的时域数据Zeromeanloglog包络线下的面积为A取包络线Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.18PSD输入谱的典型定义210110logxxGfdBGf221212121loglglglg20.30103lgoctavedecadeffffffff二倍频十倍频g2/Hzlog10(f)Gxx100010010.1.01.001log10(a)Example1ofrandomloading:20-160Hz+5dB/oct(+slope)160-800Hz0.06g2/Hz800-2000Hz-6dB/oct(-slope)Overallxxxgrms+5dB/oct(+slope)-6dB/oct(-slope)Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.19JaapWijker，RandomVibrationsinSpacecraftStructuresDesign，Page163典型PSD载荷谱(1/2)19Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.20典型PSD载荷谱(2/2)Example2ofrandomloading:Freq(Hz)g2/Hz100.1200.1500.36000.315000.1220000.121010log23.01222111mmxxGfffGfffmdB/octm为斜率Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.21典型的PSD谱及换算频率范围(Hz)谱密度(g2/Hz)10-100+3dB/oct100-6000.25600-2000-9dB/octRMS(g)14.3497频率点(Hz)谱密度(g2/Hz)100.025191000.256000.2520000.00683RMS(g)14.34970.00100.01000.10001.000010.00100.001000.0010000.00AccePSDg2/HzFrequencyHz(100,0.25)+3dB/oct(pos)-9dB/oct(neg)(600,0.25)(10,0.02519)(2000,0.00683)(RMS=14.3497g)换算Example3ofrandomloading:Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.22InputPSDSquareofTransferFunctionResponsePSD2gHz22Pag2PaHz05001000150020002500300035000204060801001201401601802004%5%6%8%Frequency(Hz)0.000.010.020.030.040.050.0601002003004005006007008009001000ABCD02040608010012014016002040608010012014016018020005001000150020002500300035000204060801001201401601802004%5%6%8%Frequency(Hz)0.000.010.020.030.040.050.0601002003004005006007008009001000ABCD020406080100120140160020406080100120140160180200通过TF计算随机振动响应calculaterandomresponseusingTF()xxS2/()rxH2/()()rrriiSHSCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.23频响函数的单位必须和PSD输入单位保持一致！频响函数的载荷类型必须和PSD的载荷类型保持一致！随机振动的单位统一23unitsm,kg,Pa,secmm,ton,MPa,secPSDin输入Specification规范g2/Hzg2/Hzg2/HzFactor转换因子×g2(9.82)/×g2(98002)Transferto转换为(m/s2)2/Hzg2/Hz(mm/s2)2/HzTF(FRF)Loadacce1m/s21g1mm/s2outputaccem/s2gmm/s2StressPa/MPaPSDout输出outputacce(m/s2)2/Hzg2/Hz(mm/s2)2/HzstressPa2/Hz/MPa2/Hz2/()()rriiSfHSfCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.24Step1：OptiStruct频响计算‒无论采用何种单位值，一律采用单位载荷激励。Step2：输入PSD激励‒激励采用闭合单位，需要模型单位相一致。‒因此一般情况下，PSD激励需转换，即将g2/Hz转换到(m/sec2)2/Hz或者(mm/sec2)2/Hz或者(in/sec2)2/Hz。Step3：PSD响应‒随机振动分析报告一般还是需要使用g为单位‒因此，一般情况下，需要将加速度PSD响应再转换回g2/Hz；加速度RMS云图同样需要转换为g。‒其它结果如应力、位移、单元力等的PSD响应和RMS结果都不需要转换。随机振动响应的推荐计算 流程 快递问题件怎么处理流程河南自建厂房流程下载关于规范招聘需求审批流程制作流程表下载邮件下载流程设计 24Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.25模型单位以mm,ton,MPa,sec单位系统为例：计算TF：1mm/s2恒定载荷计算PSD输入：将g2/Hz单位转换成(mm/s2)2/Hz单位PSD输出：‒加速度单位为mm/s2，需要转换成g‒应力单位为Mpa‒位移单位为mm随机振动的mm单位制示例2522222221/9800/sec386.4/secmmgHzHzinHzCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.26PSD曲线RMS云图随机振动的主要结果PSD曲线RMS云图Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.27PCB-randomExample2ofrandomloading:Freq(Hz)g2/Hz100.1200.1500.36000.315000.1220000.12RANDPS,10,1,1,1.0+8,0.0,9Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.28PCB-randomFREQ=1METHOD(STRUCTURE)=2RANDOM=10ACCELERATION(H3D,PHASE,PSDF)=1STRESS(H3D,PHASE,PSDF,)=2XYPLOT,ACCE,PSDF/10000(T3)SUBCASE1LABEL90005:+ZSPC=8DLOAD=6BEGINBULKFREQ110.020.050.0600.01500.0FREQ11100.0100.019FREQ4110.02000.00.033RLOAD17530ACCEDLOAD61.01.07$$RANDPScardsRANDPS10111.0+80.09$$TABLED1cardsTABLED13LinearLinear+10.01.02000.01.0ENDT$$TABRND1cardsTABRND19LOGLOG+10.00.120.00.150.00.3600.00.3+1500.00.122000.00.12ENDTCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.29多基础激励和单基础激励•SingleBase:•-extracalculationanddiskspacerequiredforeachenforcedmotionexcitation•-use“rigid”or“coupledDOF”toavoidmultipleconnectionDOFMultipleBases:-requiresseparateconnectionDOFandenforcedmotionexcitationsCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.30单基础激励，也称单点激励，各个分量的PSD响应‒位移、速度、加速度、应力、单元力等数据分量‒datacomponentsofdispl,veloc,accel,stresses,elementforces单基础激励分量的PSD响应ComponentPSDforsinglebaseexciting*//()()()()rrirjijijSfHfHfSf2/()()rriiSfHSf单点激励：其中H为传递函数，即单位载荷频响Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.31各个分量的PSD响应PSDofresponsedatacomponent‒位移、速度、加速度、应力、单元力等数据分量datacomponentsofdispl,veloc,accel,stresses,elementforces从公式中可以看出，多基础激励时需要定义CSD互谱，指明各个激励点的相互关系多基础激励的分量PSD响应compPSDresponseofMultipleBases*//()()()()rrirjijijSfHfHfSf2点激励：**/1/111/2/222**/1/212/2/121()()()()()()()()()()()()()rrrrrrrrrSfHfHfSfHfHfSfHfHfSfHfHfSfPSDCSDCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.32定义CSD函数来反应先后轮子的时延CSD的例子321.00E-081.00E-071.00E-061.00E-051.00E-041.00E-031.00E-021.00E-011.00E+000.02.04.06.08.010.0Frequency(Hz)DisplacementPSD(in2/Hz)Cross-countryroadsurfacePSDat15mphRoadRoughnessTime-domaintimedelay前轮后轮4点激励载荷组合表Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.33一般的，假设i的激励x(t)，j点的激励为x(t-)，即是激励j相对激励i的时延那么两者的CSD可以假设是相位差，那么两者的CSD可以时延信号的CSD计算33ififijiijjiiGGGeGe-2-2ififijiijjiiGGGeGe2jjiiGGCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.34Sxx，Sxy为双边功率谱密度函数，FFT为双边傅里叶变换一般信号的PSD和CSD计算2*xxxyFFTxSTFFTxFFTySTRANDPS,100,1,1,1.,0.,100RANDPS,100,2,2,1.,0.,200RANDPS,100,1,2,1.,0.,300RANDPS,100,1,2,0.,1.,400Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.强迫加速度激励加于整个地板，如右图所示不使用RBE2，直接批量选择节点加载强迫运动加载方式讨论SPCD253933131.0SPCD253935031.0SPCD253935131.0SPCD253935231.0SPCD253935931.0SPCD253938431.0SPCD253938531.0SPCD253938631.0SPCD253938731.0SPCD253940031.0SPCD253940131.0……Total4140SPCDCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.直接法频响，计算4小时没有结果改用模态法，计算24分钟后报如下错误：强迫运动加载方式讨论Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.将底面加载节点用RBE2连接起来，然后将载荷施加于RBE2中心点5分钟后正确计算出模态频响结果从而得出结论：大量自由度的强迫运动激励，通过RBE2单元进行加载更为合理强迫运动加载方式讨论Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.当采用SPCD激励时，可以要求激励自由度本身进行运动学量的输出响应结果曲线和载荷曲线在加载自由节点上应该是完全一致的！强迫运动模型的基本检查方法激励曲线Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.模态检查Unitfrf检查加速度激励，激励点的响应检查Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.InnovationIntelligence®ThankyouQuestion？