基于谐波合成法的轨道随机不平顺数值模拟
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摘要
针对轨道不平顺所致的列车随机振动问题,采用单维单变量随机场谐波合成法,引入轨道垂向、轨向及水平交叉谱的影响,以轨道不平顺谱为输入,对轨道不平顺过程进行模拟。通过对模拟样本的谱密度函数、相关函数检验验证表明,谐波合成法能有效地模拟出符合要求的随机样本,为轨道随机振动分析提供恰当的时域输入函数。以美国第6级线路轨道垂向不平顺功率谱为输入谱的数值算例,用谐波合成法模拟的轨道时域样本及其功率谱密度,与目标谱吻合较好。
Aimed at the random vibrations caused by railway tract irregularity,by introducing the cross-spectra of vertical,directional and plane railway track irregularity,and taken PSD of tract irregularity as input,stochastic track irregularity was simulated using method of 1V-1D harmonic synthesis,the validation result of the power spectral density function and the cross-correlation function of the simulation sample shows that the proposed method can simulate the target stochastic samples effectively to provide suitable input functions in time domain for railway track random vibration analysis.The numerical example of simulation of track irregularity samples in time domain and its PSD by the method of harmonic synthesis that taken American 6th grade rack vertical irregularity as inputting PSD are consistent with the goal spectrum.
Aimed at the random vibrations caused by railway tract irregularity,by introducing the cross-spectra of vertical,directional and plane railway track irregularity,and taken PSD of tract irregularity as input,stochastic track irregularity was simulated using method of 1V-1D harmonic synthesis,the validation result of the power spectral density function and the cross-correlation function of the simulation sample shows that the proposed method can simulate the target stochastic samples effectively to provide suitable input functions in time domain for railway track random vibration analysis.The numerical example of simulation of track irregularity samples in time domain and its PSD by the method of harmonic synthesis that taken American 6th grade rack vertical irregularity as inputting PSD are consistent with the goal spectrum.
引文
[1]冯军和,闫维明.列车随机激振荷载的数值模拟[J].振动与冲击,2008,27(2):49-52.FENG Junhe,YAN Weiming.Numerical Simulation for TrainStochastic Vibration Loads[J].Journal of Vibration andShock,2008,27(2):49-52.
[2]王午生.铁道线路工程[M].上海:上海科学技术出版社,1999,55-78.WANG Wusheng.Railway Lines Engineering[M].Shanghai:Shanghai Science and Technology Press,1999:55-78.
[3]ONTES R K,ENOCHSON L.Digital Time Series Analysis[M].New York:John Wiley&Sons,Inc.,1972:67-87.
[4]星谷胜.随机振动分析[M].常宝琦,译.北京:地震出版社,1977:42-62.XING Gusheng.Random Vibration Analysis[M].CHANGBaoqi,translated.Beijing:Earthquake Publishing House,1972:42-62.
[5]陈果,翟婉明.铁路轨道不平顺随机过程的数值模拟[J].西南交通大学学报,1999,34(2):138-142.CHEN Guo,ZHAI Wanming.Numerical Simulation of theStochastic Process of Railway Track Irregularities[J].Journalof Southwest Jiaotong University,1999,34(2):138-142.
[6]练松良.轨道动力学[M].上海:同济大学出版社,2003.LIAN Songliang.Track Dynamics[M].Shanghai:Tongji Uni-versity Press,2003.
[7]铁道部科学研究院.我国重载提速干线轨道不平顺功率谱密度的特征分析[R].北京:铁道科学研究院,1998.China Academy of Railway Science.The Characteristic Analy-sis of Heavy Haul Railway Track Irregularities’PSD in China[R].Beijing:China Academy of Railway Science,1998.
[8]翟婉明.车辆-轨道耦合动力学[M].北京:中国铁道出版社,2002.ZHAI Wanming.Vehicle-track Coupling Dynamics[M].Bei-jing:China Railway Publishing House,2002.
[9]陈宪麦.轨道不平顺时频域分析及预测方法的研究[D].北京:铁道部科学研究院,2006.CHEN Xianmai.Time-frequence Analysis and Prediction Studyon Track Irregularities[D].Beijing:China Academy of Rail-way Science,2006.
[10]杨文忠,练松良,刘扬.轨道不平顺功率谱拟合分析方法[J].同济大学学报:自然科学版,2006,34(3):363-367.YANG Wenzhong,LIAN Songliang,LIU Yang.Power Spec-trum Fit Analysis for Railway Track Irregularities[J].Journalof Tongji University:Natural Science Edition,2006,34(3):363-367.
[11]王福天.车辆系统动力学[M].北京:中国铁道出版社,1994.WANG Futian.Vehicle System Dynamics[M].Beijing:Chi-na Railway Publishing House,1994.
[12]POPP K,KRUSE H,KAISER I.Vehicle-track Dynamics inthe Mid-frequency Range[J].Vehicle System Dynamics,1999,31:423-464.
[13]左玉云,向俊.郑武线轨道不平顺的相关性分析[J].铁道科学与工程学报,2006,3(1):46-49.ZUO Yuyun,XIANG Jun.Correlation Analysis of Track Irregu-larities of Zhengzhou-Wuhan Railway[J].Journal of RailwayScience and Engineering,2006,3(1):46-49.
[14]SHINOZUKA M,JAN C M.Digital Simulation of Random Pro-cesses and Its Application[J].Journal of Sound and Vibra-tion,1972,25(1):111-128.
[15]SHINOZUKA M,DEODATIS G.Simulation of Stochastic Pro-cesses by Spectral Representation[J].Applied MechanicsReviews,1991,44(4):191-203.
[16]DEODATIS G.Simulation of Ergodic Multivariate StochasticProcesses[J].Journal of Engineering Mechanics,1996,122(8):778-787.
[17]肖守讷,阳光武,张卫华,等.基于谱密度函数的轨道随机不平顺仿真[J].中国铁道科学,2008,29(2):28-32.XIAO Shoune,YANG Guangwu,ZHANG Weihua.et al.Simulation of Stochastic Railway Track Irregularity Based onSpectrum Density Function[J].China Railway Science,2008,29(2):28-32.
[2]王午生.铁道线路工程[M].上海:上海科学技术出版社,1999,55-78.WANG Wusheng.Railway Lines Engineering[M].Shanghai:Shanghai Science and Technology Press,1999:55-78.
[3]ONTES R K,ENOCHSON L.Digital Time Series Analysis[M].New York:John Wiley&Sons,Inc.,1972:67-87.
[4]星谷胜.随机振动分析[M].常宝琦,译.北京:地震出版社,1977:42-62.XING Gusheng.Random Vibration Analysis[M].CHANGBaoqi,translated.Beijing:Earthquake Publishing House,1972:42-62.
[5]陈果,翟婉明.铁路轨道不平顺随机过程的数值模拟[J].西南交通大学学报,1999,34(2):138-142.CHEN Guo,ZHAI Wanming.Numerical Simulation of theStochastic Process of Railway Track Irregularities[J].Journalof Southwest Jiaotong University,1999,34(2):138-142.
[6]练松良.轨道动力学[M].上海:同济大学出版社,2003.LIAN Songliang.Track Dynamics[M].Shanghai:Tongji Uni-versity Press,2003.
[7]铁道部科学研究院.我国重载提速干线轨道不平顺功率谱密度的特征分析[R].北京:铁道科学研究院,1998.China Academy of Railway Science.The Characteristic Analy-sis of Heavy Haul Railway Track Irregularities’PSD in China[R].Beijing:China Academy of Railway Science,1998.
[8]翟婉明.车辆-轨道耦合动力学[M].北京:中国铁道出版社,2002.ZHAI Wanming.Vehicle-track Coupling Dynamics[M].Bei-jing:China Railway Publishing House,2002.
[9]陈宪麦.轨道不平顺时频域分析及预测方法的研究[D].北京:铁道部科学研究院,2006.CHEN Xianmai.Time-frequence Analysis and Prediction Studyon Track Irregularities[D].Beijing:China Academy of Rail-way Science,2006.
[10]杨文忠,练松良,刘扬.轨道不平顺功率谱拟合分析方法[J].同济大学学报:自然科学版,2006,34(3):363-367.YANG Wenzhong,LIAN Songliang,LIU Yang.Power Spec-trum Fit Analysis for Railway Track Irregularities[J].Journalof Tongji University:Natural Science Edition,2006,34(3):363-367.
[11]王福天.车辆系统动力学[M].北京:中国铁道出版社,1994.WANG Futian.Vehicle System Dynamics[M].Beijing:Chi-na Railway Publishing House,1994.
[12]POPP K,KRUSE H,KAISER I.Vehicle-track Dynamics inthe Mid-frequency Range[J].Vehicle System Dynamics,1999,31:423-464.
[13]左玉云,向俊.郑武线轨道不平顺的相关性分析[J].铁道科学与工程学报,2006,3(1):46-49.ZUO Yuyun,XIANG Jun.Correlation Analysis of Track Irregu-larities of Zhengzhou-Wuhan Railway[J].Journal of RailwayScience and Engineering,2006,3(1):46-49.
[14]SHINOZUKA M,JAN C M.Digital Simulation of Random Pro-cesses and Its Application[J].Journal of Sound and Vibra-tion,1972,25(1):111-128.
[15]SHINOZUKA M,DEODATIS G.Simulation of Stochastic Pro-cesses by Spectral Representation[J].Applied MechanicsReviews,1991,44(4):191-203.
[16]DEODATIS G.Simulation of Ergodic Multivariate StochasticProcesses[J].Journal of Engineering Mechanics,1996,122(8):778-787.
[17]肖守讷,阳光武,张卫华,等.基于谱密度函数的轨道随机不平顺仿真[J].中国铁道科学,2008,29(2):28-32.XIAO Shoune,YANG Guangwu,ZHANG Weihua.et al.Simulation of Stochastic Railway Track Irregularity Based onSpectrum Density Function[J].China Railway Science,2008,29(2):28-32.
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