车辆-轨道系统时-空随机分析模型
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摘要
车辆-轨道耦合系统具有时-空域的随机特征。为了更好地研究车辆-轨道系统的时-空随机演化过程,提出车辆-轨道系统时-空随机分析模型。该模型将车辆-轨道耦合系统分为车辆子系统、轨道子系统及轮轨界面系统,可考虑车辆系统、线路系统参数的随机性及轨道随机不平顺的时变性,同时采用数论法实现不同动力参数的组合,用概率密度演化方程解决系统激励输入与响应输出的概率密度传递问题。最后,采用该模型分析了不同变异系数下的车辆-轨道系统时-空随机振动,分析中假定系统动力参数服从正态分布,并基于实测数据进行轨道不平顺的时-空随机模拟。结果表明:依据本文模型得到的计算结果符合物理概念;由于动力参数的随机变异性直接与时间相关,使得利用此随机分析模型,探讨系统动力响应的随机演化机制、制定考虑长时效的系统动力指标限值及养修计划成为可能。建议完善车线系统参数的基础检测资料。
Vehicle-track coupled system has the random nature in time-space domain.In order to better study the stochastic temporal-spatial evolution process of the vehicle-track systems,this paper proposed a computational model for analyzing temporal-spatial stochastic vibrations of vehicle-track system,which divided the vehicle-track system into vehicle subsystem,track subsystem,and wheel-rail interfacial subsystem,and considered the randomness of the dynamic parameters of vehicle system,the track system and the time variation of the track stochastic irregularity.A numerical theory method was used to ensemble different dynamic parameters.Then the probability density evolution equation was implemented to solve the delivery problem of probability density between excitation inputs and response outputs.Finally,an analysis was carried out on the temporal-spatial stochastic vibrations of vehicle-track systems subjected to different coefficients of variation,in which the dynamic parameters were assumed to be subject to normal distribution,and the time-space stochastic simulation of track irregularities was conducted based on measured data.The results show that the computed results obtained from this model accord with physical conceptions.Due to direct relation of the random variability of dynamic parameters with time,it is possible to explore the temporal-spatial stochastic evolutionary mechanism and formulate the dynamic indices limits by adopting time-space stochastic computation model.It is recommended to improve the basic testing data of vehicle-track system parameters.
Vehicle-track coupled system has the random nature in time-space domain.In order to better study the stochastic temporal-spatial evolution process of the vehicle-track systems,this paper proposed a computational model for analyzing temporal-spatial stochastic vibrations of vehicle-track system,which divided the vehicle-track system into vehicle subsystem,track subsystem,and wheel-rail interfacial subsystem,and considered the randomness of the dynamic parameters of vehicle system,the track system and the time variation of the track stochastic irregularity.A numerical theory method was used to ensemble different dynamic parameters.Then the probability density evolution equation was implemented to solve the delivery problem of probability density between excitation inputs and response outputs.Finally,an analysis was carried out on the temporal-spatial stochastic vibrations of vehicle-track systems subjected to different coefficients of variation,in which the dynamic parameters were assumed to be subject to normal distribution,and the time-space stochastic simulation of track irregularities was conducted based on measured data.The results show that the computed results obtained from this model accord with physical conceptions.Due to direct relation of the random variability of dynamic parameters with time,it is possible to explore the temporal-spatial stochastic evolutionary mechanism and formulate the dynamic indices limits by adopting time-space stochastic computation model.It is recommended to improve the basic testing data of vehicle-track system parameters.
引文
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[14]XU L,CHEN Z,ZHAI W.An Advanced Vehicle-slab Track Interaction Model Considering Rail Random Irregularities[J].Journal of Vibration and Control,2017:1-12.(DOI:10.1177/1077546317731005)
[15]XU L,ZHAI W,GAO J.A Probabilistic Model for Track Random Irregularities in Vehicle/track Coupled Dynamics[J].Applied Mathematical Modelling,2017,51:145-158.
[16]LI J,CHEN J B.The Dimension-reduction Strategy via Mapping for Probability Density Evolution Analysis of Nonlinear Stochastic Systems[J].Probabilistic Engineering Mechanics,2006,21(4):442-453.
[17]华罗庚,王元.数论在近似分析中的应用[M].北京:科学出版社,1978.
[18]李杰,陈建兵.随机结构非线性动力响应的概率密度演化分析[J].力学学报,2003,35(6):716-722.LI Jie,CHEN Jianbing.The Probability Density Evolution Method for Analysis of Dynamic Nonlinear Response of Stochastic Structures[J].Chinese Journal of Theoretical and Applied Mechanics,2003,35(6):716-722.
[19]LI J,CHEN J B.The Principle of Preservation of Probability and the Generalized Density Evolution Equation[J].Structural Safety,2008,30:65-77.
[20]SOONG T T.Random Differential Equations in Science and Engineering[M].New York:Academic Press,1973.
[21]张涵信,沈孟育.计算流体力学[M].北京:国防工业出版社,2003:134-172.
[2]余志武,毛建锋,谈遂,等.车辆参数随机的车桥竖向随机振动分析[J].铁道学报,2015,37(1):97-104.YU Zhiwu,MAO Jianfeng,TAN Sui,et al.The Stochastic Analysis of the Track-bridge Vertical Coupled Vibration with Random Train Parameters[J].Journal of the China Railway Society,2015,37(1):97-104.
[3]李秋义.高速铁路无缝线路动力稳定性概率分析理论研究[D].长沙:中南大学,2003.
[4]RICCIARDI G.Random Vibration of Beam under Moving Loads[J].Journal of Engineering Mechanics,1994,120(11):2361-2380.
[5]SAEED M,SOODABEH G.Estimation of Train Derailment Probability Using Rail Profile Alterations[J].Structure and Infrastructure Engineering,2012,8(11):1034-1053.
[6]翟婉明.车辆-轨道耦合动力学[M].4版.北京:科学出版社,2015.
[7]XU L,ZHAI W.A Novel Model for Determining the Amplitude-wavelength Limits of Track Irregularities Accompanied by a Reliability Assessment in Railway Vehicletrack Dynamics[J].Mechanical Systems and Signal Processing,2017,86:260-277.
[8]CHEN G,ZHAI W M.A New Wheel/Rail Spatially Dynamic Coupling Model and Its Verification[J].Vehicle System Dynamics,2004,41(4):301-322.
[9]SHEN Z Y,HEDRICK J K,ELKINS J A.A Comparison of Alternative Creep Force Models for Rail Vehicle Dynamic Analysis[C]//Proceedings of 8th IAVSD Symposium.Cambridge:Taylor&Francis,1983:591-605.
[10]徐磊,翟婉明.轨道结构随机场模型与车辆-轨道耦合随机动力分析[J].应用数学与力学,2017,38(1):67-74.XU Lei,ZHAI Wanming.The Random Field Model for Track Structures and Vehicle-track Coupled Stochastic Dynamic Analysis[J].Applied Mathematics and Mechanics,2017,38(1):67-74.
[11]文德智,卓仁鸿,丁大杰,等.蒙特卡罗模拟中相关变量随机数序列的产生方法[J].物理学报,2012,61(22):1-8.WEN Dezhi,ZHUO Renhong,DING Dajie,et al.Generation of Correlated Pseudorandom Variables in Monte Carlo Simulation[J].Acta Physica Sinica,2012,61(22):1-8.
[12]王梓坤.概率论基础及其应用[M].3版.北京:北京师范大学出版社,2007.
[13]郑铎,吴世伟.正态分布函数计算的建议及其反函数的非迭代算法[J].河海大学学报,1993,21(2):61-64.ZHENG Duo,WU Shiwei.A Proposal for Computing Normal Distribution Function and a Non-iterative Method of Its Inverse Function[J].Journal of Hohai University,1993,21(2):61-64.
[14]XU L,CHEN Z,ZHAI W.An Advanced Vehicle-slab Track Interaction Model Considering Rail Random Irregularities[J].Journal of Vibration and Control,2017:1-12.(DOI:10.1177/1077546317731005)
[15]XU L,ZHAI W,GAO J.A Probabilistic Model for Track Random Irregularities in Vehicle/track Coupled Dynamics[J].Applied Mathematical Modelling,2017,51:145-158.
[16]LI J,CHEN J B.The Dimension-reduction Strategy via Mapping for Probability Density Evolution Analysis of Nonlinear Stochastic Systems[J].Probabilistic Engineering Mechanics,2006,21(4):442-453.
[17]华罗庚,王元.数论在近似分析中的应用[M].北京:科学出版社,1978.
[18]李杰,陈建兵.随机结构非线性动力响应的概率密度演化分析[J].力学学报,2003,35(6):716-722.LI Jie,CHEN Jianbing.The Probability Density Evolution Method for Analysis of Dynamic Nonlinear Response of Stochastic Structures[J].Chinese Journal of Theoretical and Applied Mechanics,2003,35(6):716-722.
[19]LI J,CHEN J B.The Principle of Preservation of Probability and the Generalized Density Evolution Equation[J].Structural Safety,2008,30:65-77.
[20]SOONG T T.Random Differential Equations in Science and Engineering[M].New York:Academic Press,1973.
[21]张涵信,沈孟育.计算流体力学[M].北京:国防工业出版社,2003:134-172.