OptiStruct随机振动分析

InnovationIntelligence®OptiStruct随机振动分析马越峰[e-mail]@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.Allrightsr