轨道不平顺激励下车辆-桥梁垂向随机振动方差解法
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摘要
提出时滞多维非白噪声轨道不平顺激励下车辆-桥梁垂向随机振动的时域分析方法。采用白噪声滤波法模拟单轮对下的不平顺,在宽频带内识别滤波器参数以实现波长选择功能。基于Pade近似构造累次时滞滤波器以反映各轮对下不平顺之间的时滞关系。结合成型和时滞滤波器,构造以一致白噪声为输入、时滞多维非白噪声不平顺为输出的合成滤波器。建立车辆-桥梁垂向振动模型,并与合成滤波器联立得到一致白噪声激励下的车-桥-滤波器扩阶状态方程。继而提出求解此扩阶时变系统随机振动方差响应的递推算法。算例结果与MonteCarlo模拟法符合良好,表明该方法具有足够的精度,且对时间步长不敏感。
A time domain method was proposed for analyzing the vehicle-bridge stochastic vibration excited by multidimensional time-delay nonwhite rail irregularities.The rail irregularity under a single wheelset was produced by the white noise filtration method.And the parameters of the shape filter were identified in a wide frequency range to realize wavelength selection.Based on the high order Pade approximation,a stepwise time-delay filter was constructed to reflect time-delays among irregularities under different wheelsets.A combined filter with uniform white noise input to generate multidimensional time-delay nonwhite rail irregularities was constructed by combining the shape filter and the time-delay filter.The vehicle-bridge vertical dynamic model was established,and was integrated into the combined filter to obtain the expanded order vehicle-bridge-filter state-space equation.Then,a covariance recursive method for the stochastic vibration analysis of the expanded time-variant system was suggested.Numerical results accord well with the Monte Carlo simulation method,which indicates the high accuracy of the proposed method.In addition,the method shows no sensitivity to the time step size.
A time domain method was proposed for analyzing the vehicle-bridge stochastic vibration excited by multidimensional time-delay nonwhite rail irregularities.The rail irregularity under a single wheelset was produced by the white noise filtration method.And the parameters of the shape filter were identified in a wide frequency range to realize wavelength selection.Based on the high order Pade approximation,a stepwise time-delay filter was constructed to reflect time-delays among irregularities under different wheelsets.A combined filter with uniform white noise input to generate multidimensional time-delay nonwhite rail irregularities was constructed by combining the shape filter and the time-delay filter.The vehicle-bridge vertical dynamic model was established,and was integrated into the combined filter to obtain the expanded order vehicle-bridge-filter state-space equation.Then,a covariance recursive method for the stochastic vibration analysis of the expanded time-variant system was suggested.Numerical results accord well with the Monte Carlo simulation method,which indicates the high accuracy of the proposed method.In addition,the method shows no sensitivity to the time step size.
引文
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[15]沈锐利.高速铁路桥梁与车辆耦合振动研究[D].成都:西南交通大学,1998.26-27.
[16]陈果.车辆-轨道耦合系统随机振动分析[D].成都:西南交通大学,2000:26-27,94.
[17]王生泽.线性的变振动系统动力学方程的一类解法———区间状态转移矩阵逼近算法[J].东华大学学报(自然科学版),1998,24(3):67-73.WANG Sheng-ze.An Algorithm for the Dynamic Re-sponse of Linear Ti me-varying Vibration Systems———AnAlgorithm Based on Approxi mation of the State Transi-tion Matrixin a Small Period of Ti me[J].Journal of Don-ghua University,Natural Science,1998,24(3):67-73.
[18]克拉夫R W,彭津J.结构动力学[M].王光远,等译.北京:科学出版社,1981.308-310.
[19]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004:63-65.
[2]夏禾.车辆与结构动力相互作用[M].第二版.北京:科学出版社,2005.187-190.
[3]曾庆元,向俊,娄平.车桥及车轨时变系统横向振动计算中的根本问题与列车脱轨能量随机分析理论[J].中国铁道科学,2002,23(1):1-10.ZENG Qing-yuan,XIANG Jun,LOU Ping.FundamentalProblems in Calculation of Transverse Vibration of Train-bridge and Train-track Ti me-varying Systemand Theory ofEnergy Random Analysis for Train Derail ment[J].ChinaRail way Science,2002,23(1):1-10.
[4]夏禾,张宏杰,曹艳梅,等.车桥耦合系统在随机激励下的动力分析及其应用[J].工程力学,2003,20(3):142-149.XIA He,ZHANG Hong-jie,CAO Yan-mei,et al.Dy-namic Analysis of Train-Bridge System Under Random Ex-citations[J].Engineering Mechanics.2003,20(3):142-149.
[5]丁建华,李冀龙,高农.车流作用下简支桥梁的随机振动分析[J].哈尔滨建筑大学学报,1997,30(2):109-114.DINGJian-hua,LI Ji-long,GAO Nong.Random Analysisof Si mple Beam Bridges Under Vehicle Flow Loads[J].Journal of Harbin University of Civil Engineering and Ar-chitecture.1997,30(2):109-114.
[6]孙璐,邓学钧.移动的车辆随机荷载作用下梁桥的瞬态响应[J].振动与冲击,1997,16(1):62-68.SUN Lu,DENG Xue-jun.Transient Response of Bridge toTravelling Random Vehicle Loads[J].Journal of Vibrationand Shock.1997,16(1):62-68.
[7]Wang R T,Lin T Y.Random Vibration of Multi-spanTi moshenko Beam Due to a Moving Load[J].Journal ofSound and Vibration,1998,213(1):127-138.
[8]Zibdeh HS.Dynamic Response of a Rotating BeamSubjec-ted to a Random Moving Load[J].Journal of Sound andVibration,1999,223(5):741-758.
[9]Abu-Hilal M.Vibration of Beams with General BoundaryConditions Due to a Moving Random Load[J].Archive ofApplied Mechanics,2003,72(9):637-650.
[10]Di Paola M,Ricciardi G.Vibration of a Bridge Under aRandom Train of Moving Loads[C]//ASCE.Proceedingsof the 6th ASCE Specialty Conference on ProbabilisticMechanics,Structural and Geotechnical Reliability.NewYork:ASCE,1992:136-139.
[11]小西一郎(日).钢桥(第七分册)[M].韩毅,等译.北京中国铁道出版社,1982.
[12]方同,冷小磊,李军强,等.演变随机响应问题的统一解法[J].振动工程学报,2002,15(3):290-294.FANG Tong,LENG Xiao-lei,LI Jun-qiang,et al.A Unified Approach to Evolutionary Random Response Problem[J].Journal of Vibration Engineering,2002,15(3)290-294.
[13]李鸿晶,孙广俊.结构平稳随机地震反应时域分析:方法[J].地震工程与工程振动,2005,25(4):31-36.LI Hong-jing,SUN Guang-jun.Random Seismic Response Analysis of Structures in Ti me Domain:Methodology[J].Earthquake Engineering and Engineering Vibration,2005,25(4):31-36.
[14]Faisal O,Sesharis.Opti mization of a Tractor-semitrailePassive Suspension Using Covariance Analysis Techniqu[J].Society of Automotive Engineers,Paper 942304.
[15]沈锐利.高速铁路桥梁与车辆耦合振动研究[D].成都:西南交通大学,1998.26-27.
[16]陈果.车辆-轨道耦合系统随机振动分析[D].成都:西南交通大学,2000:26-27,94.
[17]王生泽.线性的变振动系统动力学方程的一类解法———区间状态转移矩阵逼近算法[J].东华大学学报(自然科学版),1998,24(3):67-73.WANG Sheng-ze.An Algorithm for the Dynamic Re-sponse of Linear Ti me-varying Vibration Systems———AnAlgorithm Based on Approxi mation of the State Transi-tion Matrixin a Small Period of Ti me[J].Journal of Don-ghua University,Natural Science,1998,24(3):67-73.
[18]克拉夫R W,彭津J.结构动力学[M].王光远,等译.北京:科学出版社,1981.308-310.
[19]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004:63-65.
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