Altair随机振动资料

Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.SEC8随机振动分析Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.2数据分类ClassificationofPhysicalDataRandomStationaryNon-StationaryNon-ErgodicDeterministicPhysicalDataRandomvibrationErgodic各态历经过程ShockSpectrumTransientReproducethedatabycontrolledexperiments可控性FrequencyCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.3StationaryandErgodic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.4各态历经随机信号，N(µ,σ)ErgodicRandomsignal4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.5正态分布的特征charactersofnormaldistribution5平均值的影响标准差的影响Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.6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6Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.7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.8随机振动结果的常用置信水平Commonconfidencelevelforrandomvibration82221()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.9PSD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.10PSD计算公式PSDFunctionCalculation10双边谱1()()2ixxxxSRdePSD使用单边谱2000xxxxSG21()xxSFFTxtTCopyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.11如何生成PSD载荷ConverttimerecordstoPSD11PSD(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.12PSD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.13JaapWijker，RandomVibrationsinSpacecraftStructuresDesign，Page163典型PSD载荷谱(1/2)13Copyright©2013AltairEngineering,Inc.ProprietaryandConfidential.Allrightsreserved.14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.15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.16InputPSDSquareofTransferFunctionResponsePSD2gHz22Pag2PaHz05001000150020002500300035000204060801001201401601802004%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.17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！随机振动的单位统一17unitsm,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.18Step1：OptiStruct频响计算‒无论采用何种单位值，一律采用单位载