高速列车-桥梁竖向随机振动的时域分析方法
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摘要
提出时间相关多维有色噪声形式的轨道不平顺激励下列车-桥梁耦合系统协方差响应的时域递推方法。用白噪声滤波法生成轨道不平顺有色噪声过程,在宽频带内识别滤波器参数以同时实现滤波成型和波长截断功能。提出基于高阶Pade近似的累次时滞系统,以实现列车多轮对下轨道不平顺激励的大时滞再现;再结合成型滤波器构造列车下轨道不平顺激励的一致白噪声模型。建立列车-桥梁垂向振动的状态方程,将其与激励模型联立得到一致白噪声激励下的列车-桥梁扩阶状态方程。将方差递推法推广到时变系统,求解列车-桥梁系统的随机振动。分析结果与Monte Carlo模拟法符合良好,表明了方法的正确性。
A time domain covariance method for the trainbridge vertical stochastic vibration excited by the time-correlated multidimensional nonwhite noise rail irregularity was proposed.The parameter identification of the shape filter producing the nonwhite rail irregularity was carried out in a wide frequency range to realize the shape filtering and the wavelength truncation together.A stepwise time-delay system based on the high order Pade approximation was proposed to simulate the large time-delay excitations under railway trains.The authors combine the shape filter and time-delay system to construct the rail irregularity model with uniform white noise input.The state-space equation of train-bridge vertical vibration was derived,and was integrated with the excitation model to obtain the expanded order train-bridge-excitation state-space equation with uniform white noise disturbance.By extending the recursive covariance method to time-variant system,the covariance response of train-bridgeexcitation system was obtained.Numerical results coincide with the Monte Carlo simulation.This indicats the correctness of the method.
A time domain covariance method for the trainbridge vertical stochastic vibration excited by the time-correlated multidimensional nonwhite noise rail irregularity was proposed.The parameter identification of the shape filter producing the nonwhite rail irregularity was carried out in a wide frequency range to realize the shape filtering and the wavelength truncation together.A stepwise time-delay system based on the high order Pade approximation was proposed to simulate the large time-delay excitations under railway trains.The authors combine the shape filter and time-delay system to construct the rail irregularity model with uniform white noise input.The state-space equation of train-bridge vertical vibration was derived,and was integrated with the excitation model to obtain the expanded order train-bridge-excitation state-space equation with uniform white noise disturbance.By extending the recursive covariance method to time-variant system,the covariance response of train-bridgeexcitation system was obtained.Numerical results coincide with the Monte Carlo simulation.This indicats the correctness of the method.
引文
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[6]Zibdeh HS.Dynamic response of a rotating beam subjected to a random moving load[J].Journal of Sound and Vibration,1999,223(5):741-758.
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[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.
[14]Faisal O,Seshadris.Optimization of a tractor-semitrailer passive suspension using covariance analysis technique[J].SAE Paper,942304:534-548.
[15]周劲松,张洪,沈钢,等.基于轨道谱的铁道车辆主动悬挂轴间预瞄控制[J].同济大学学报,2006,34(2):239-243.
[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.
[17]王生泽.线性时变振动系统动力学方程的一类解法[J].中国纺织大学学报,1998,24(3):67-73.
[18]Clough R W,Penzien J.结构动力学[M].王光远,等译.北京:科学出版社,1981:308-310.
[19]陈泽深,王成国.铁道车辆动力学与控制[M].北京:中国铁道出版社,2004:177.
[2]李小珍,强士中.列车-桥梁耦合振动研究的现状与发展趋势[J].铁道学报,2002,24(5):112-120.
[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.
[4]Fryba L.Non-stationary response of a beam to moving random force[J].Journal of Sound and Vibration,1976,46(3):328-338.
[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.
[6]Zibdeh HS.Dynamic response of a rotating beam subjected to a random moving load[J].Journal of Sound and Vibration,1999,223(5):741-758.
[7]Abu-Hilal M.Vibration of beams with general boundary conditions due to a moving random load[J].Archive of Applied Mechanics,2003,72(9):637-650.
[8]小西一郎(日)编.韩毅等译.钢桥(第七分册)[M].北京:中国铁道出版社,1982.
[9]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.
[10]谭东耀,杨庆山.动力系统在时间相关荷载激发下随机振动的离散分析法[J].地震工程与工程振动;1990,10(2):37-45.
[11]S To C W.A Stochasic version of the Newmark family of algorithms for discretized dynamic systems[J].Computer and Structure,1992,44(3):667-673.
[12]欧进萍,王光远.结构随机振动[M].北京:高等教育出版社,1998:189-197.
[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.
[14]Faisal O,Seshadris.Optimization of a tractor-semitrailer passive suspension using covariance analysis technique[J].SAE Paper,942304:534-548.
[15]周劲松,张洪,沈钢,等.基于轨道谱的铁道车辆主动悬挂轴间预瞄控制[J].同济大学学报,2006,34(2):239-243.
[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.
[17]王生泽.线性时变振动系统动力学方程的一类解法[J].中国纺织大学学报,1998,24(3):67-73.
[18]Clough R W,Penzien J.结构动力学[M].王光远,等译.北京:科学出版社,1981:308-310.
[19]陈泽深,王成国.铁道车辆动力学与控制[M].北京:中国铁道出版社,2004:177.
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