OptiStruct随机振动分析

28-April-2014OptiStructInnovationIntelligence®随机振动分析马越峰yuefeng.ma@altair.com.cnsupport@altair.com.cn(supportemail)4006-196-186(supporthotline)振动分类—按载荷形式和响应类型Classificationofvibration线性系统LinearsystemMxCxKxf()t正则模态分析自由振动RealEigen/ModesFreeVibration复模态分析(f=0)ComplexEigen/Modes瞬态响应Transientresponse精确分析频率响应强迫振动外力、压强()FrequencyresponseEnforcedVibration(Force,Pressure)随机振动响应统计分析RandomResponseDynamicresponseDynamic强迫运动(加速度、位移)EnforcedMotion(Acceleration,Displacement)峰值分析响应谱等SRS,DDAM2Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.2强迫振动？强迫运动激励？强迫运动激励首先一定是固定在某些“基础”之上的。Lunchload地震波Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.强迫运动–虚拟约束法SPCD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：Zdirection‒SPCD定义节点1的强迫运动位移Node1‒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？Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.强迫运动–虚拟约束法SPCD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ZdirectionNode1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.强迫运动的绝对响应和相对响应惯性系非惯性系ugr()()tut质点位移u()()()tututrgutr()参质点加速度u()()()tutut质量Mrg考轴惯性力fImur()()tmugt阻尼C弹性恢复力fsrku()txglobalut()阻尼力gfdrcu()t运动方程murcurkurmugpeffCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.6PARAM,ENFMOTN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。Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.7数据分类ClassificationofPhysicalDataPhysicalDataReproducethedatabycontrolledexperiments可控性RandomDeterministicTransientStationaryNon-StationaryFrequencyShockSpectrumNon-ErgodicErgodic各态历经过程RandomvibrationCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.8StationaryandErgodic稳态数据和各态历经过程数据采样asample(realization,record)oftherandomprocess•Stationary:Foreveryt,PDF(ProbabilityDensityFunction),xand2xofeveryrecordareconstant.对每个采样数据，概率密度函数，2x和x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Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.9各态历经随机信号，N(µ,σ)ErgodicRandomsignalacceacceµ0PdfTimex()x2n1212F()xe2dxaRMSni2i1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(标准差Standarddeviation)：每个样本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1010Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.正态分布的特征charactersofnormaldistribution平均值的影响标准差的影响11Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.11随机振动响应的两个基本假设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12Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.12正态分布的置信水平1σ~3σ安全区域危险区域0.135%危险区域0.135%99.73%65σ4321123456x()x2σP(|x|σ)P(|x|>σ)PerMillion/每百万12F()xe2dx1σ68.27%31.7%317,3002σ95.45%4.55%45,50022.5σ98.76%1.24%12,400n123σ99.73%0.27%2,700RMSaini13.5σ99.953%0.047%4704σ99.9937%0.0063%63随机振动采用双边置信水平5σ99.999943%0.000057%0.576σ99.9999998%0.0000002%0.002Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.13随机振动结果的常用置信水平Commonconfidencelevelforrandomvibrationacceacce+g3σ2σσµ=0Pdf-gTimexx2σ安全率失效率122F()xedx2.5σ98.76%1.24%2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14Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.14PSD定义公式PSDFunctiondefinitionT/2自相关函数：1Rxx()Extxtlimx(t)xtdtt(Auto)correctionTT/22222xxRRRxx()xx,xx()xx(0)自功率谱密度函数定义1iSxx()()Rxxd(Auto)PSD2ePSDiRxx()()SxxdAeRMSAAff12Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.15PSD计算公式PSDFunctionCalculation1i双边谱Sxx()()Rxxd2e2Sxx0PSD使用单边谱Gxx0012SFFTx(t)xxT16Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.16如何生成PSD载荷ConverttimerecordstoPSD不同路面的时域数据ZeromeanPSDAInputPSD=(g2)/HzEnvelopecurve包络线取包络线包络线下的面积为Alogff1log217Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.17PSD输入谱的典型定义二倍频octavelogExample1ofrandomloading:2ff2120-160Hz+5dB/oct(+slope)lgfflgff2121160-800Hz0.06g2/Hzlg20.30103800-2000Hz-6dB/oct(-slope)Overallxxxgrms十倍频decadelgff212Gxx.1g/HzGfx2dB10log10Gfx1+5dB/oct(+slope)-6dB/oct(-slope).01log10(a).001101001000log10(f)Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.18典型PSD载荷谱(1/2)JaapWijker，RandomVibrationsinSpacecraftStructuresDesign，Page16319Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.19典型PSD载荷谱(2/2)Example2ofrandomloading:Freq(Hz)g2/Hz100.1200.1mdB/oct500.36000.315000.1220000.12mm10log1023.01Gfx2ff22m为斜率Gxf1f1f1Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.20典型的PSD谱及换算Example3ofrandomloading:2频率范围(Hz)谱密度(g/Hz)1.000010-100+3dB/oct(100,0.25)(600,0.25)100-6000.25600-2000-9dB/oct0.1000+3dB/octRMS(g)14.3497(pos)-9dB/oct(neg)/Hz2换算g(10,0.02519)AcceAccePSD(2000,0.00683)0.0100频率点(Hz)谱密度(g2/Hz)100.025191000.250.00106000.2510.00100.00Frequency1000.0010000.00Hz(RMS=14.3497g)20000.00683RMS(g)14.3497Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.21通过TF计算随机振动响应calculaterandomresponseusingTF0.062Bg0.05Hz0.04AInputPSD0.030.02SxxC()0.01D0.0035000100200300400500600700800900100023000Frequency(Hz)4%Pa25002g20005%SquareofTransferFunction150026%1000Hrx/()5008%00204060801001201401601802001601402120Pa10080ResponsePSDHz6040220SHSrr()()r/ii0020406080100120140160180200Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.22随机振动的单位统一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！2Sr()()fHr/iSifunitsm,kg,Pa,secmm,ton,MPa,secSpecification规范g2/Hzg2/Hzg2/HzPSDinFactor转换因子×g2(9.82)/×g2(98002)输入Transferto转换为(m/s2)2/Hzg2/Hz(mm/s2)2/HzLoadacce1m/s21g1mm/s2TFaccem/s2gmm/s2(FRF)outputStressPa/MPaPSDacce(m/s2)2/Hzg2/Hz(mm/s2)2/Hzoutoutput输出22stressPa/Hz/MPa/Hz23Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.23随机振动响应的推荐计算流程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 成本分析报告下载顾客满意度调查结果及分析报告员工思想动态分析报告期中考试质量分析报告高一期中考试质量分析报告 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。2424Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.随机振动的mm单位制示例模型单位以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mm222mm1g/Hz98002/Hzsec22in386.42/Hzsec25Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.25随机振动的主要结果PSD曲线PSD曲线RMS云图RMS云图Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.26PCB-randomExample2ofrandomloading:Freq(Hz)g2/Hz100.1200.1500.36000.315000.1220000.12RANDPS,10,1,1,1.0+8,0.0,9Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.27PCB-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.28多基础激励和单基础激励•SingleBase:•-extracalculationanddiskspacerequiredforeachenforcedmotionexcitation•-use“rigid”or“coupledDOF”toavoidmultipleconnectionDOFMultipleBases:-requiresseparateconnectionDOFandenforcedmotionexcitationsCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.29单基础激励分量的PSD响应ComponentPSDforsinglebaseexciting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*Sr()()()()fHr//ifHrjfSijfij2单点激励：Sr()()fHr/iSif其中H为传递函数，即单位载荷频响Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.30多基础激励的分量PSD响应compPSDresponseofMultipleBases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,elementforcesS()()()()fH*fHfSfrr//irjijij**Sfr()()()()()()()HfHfSfHfHfSfr/1r/111r/2r/222PSD2点激励：**HfHfSfHfHfSf()()()()()()CSDr/1r/212r/2r/121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Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.31CSD的例子定义CSD函数来反应先后轮子的时延4点激励载荷组合表Cross-countryroadsurfacePSDat15mph1.00E+001.00E-011.00E-02/Hz)21.00E-031.00E-041.00E-051.00E-06Time-domainDisplacement(inPSD1.00E-07前轮1.00E-080.02.04.06.08.010.0Frequency(Hz)后轮RoadRoughnesstimedelay32Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.32时延信号的CSD计算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2GGjjii那么两者的CSD可以-i2f-i2fGijGiiGjjeGiie假设是相位差，那么两者的CSD可以ififGijGiiGjjeGiie33Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.33一般信号的PSD和CSD计算Sxx，Sxy为双边功率谱密度函数，FFT为双边傅里叶变换2FFTxSxxTFFTxFFT*ySxyTRANDPS,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.34强迫运动加载方式讨论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SPCD253933131.0SPCD253935031.0SPCD253935131.0SPCD253935231.0SPCD253935931.0SPCD253938431.0SPCD253938531.0SPCD253938631.0SPCD253938731.0SPCD253940031.0SPCD253940131.0……Total4140SPCDCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.强迫运动加载方式讨论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：Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.强迫运动加载方式讨论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Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.强迫运动模型的基本检查方法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！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.ThankyouQuestion？InnovationIntelligence®Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.