轨道不平顺激励下不确定车轨耦合系统动力分析
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摘要
对于具有不确定参数车轨耦合系统,论文建立了随机轨道不平顺激励下耦合系统动力响应预测的虚拟激励摄动算法.车辆采用多刚体系统模型,其参数的不确定性以随机变量形式描述.弹性轨道视为无限长周期结构,建立哈密顿对偶坐标体系下轨道典型子结构状态运动方程.采用线性赫兹理论建立轮轨关系,得到混合坐标下车轨耦合系统运动方程.轨道不平顺视为平稳随机过程,根据虚拟激励法原理,可将其转化为虚拟简谐激励.基于虚拟激励法推导了随机响应的高阶敏度,提出了不确定车轨耦合系统在轨道不平顺激励下结构响应预测的高阶虚拟激励摄动方法,数值结果同蒙特卡洛方法进行了对比,结论表明所提出的方法具有很好的精度.
In this paper pseudo excitation-perturbation method was established for coupled vehicletrack systems with parameter uncertainties subjected to random track irregularity.The vehicle system was simplified as a multiple rigid-body model whose uncertainty of parameters was described by random variables.The track was regarded as an infinitely long periodic structure,and the state equation of typical substructure of the track was established in Hamiltonian system.Using the linear Hertz theory,the dynamic equation of coupled vehicle-track systems under mixed coordinate was established by wheel-rail coupling characteristics.Base on the pseudo excitation method the track irregularity was regarded as the stationary random process which can be transformed as pseudo harmonic,also the high order sensitivity of random response was obtained.Then perturbation method was used to compute the random vibration responses of coupled vehicle-track systems with parameter uncertainties subjected to track irregularity.In the Numerical example the efficiency and computational accuracy are demonstrated by Monte Carlo Simulation approaches.
In this paper pseudo excitation-perturbation method was established for coupled vehicletrack systems with parameter uncertainties subjected to random track irregularity.The vehicle system was simplified as a multiple rigid-body model whose uncertainty of parameters was described by random variables.The track was regarded as an infinitely long periodic structure,and the state equation of typical substructure of the track was established in Hamiltonian system.Using the linear Hertz theory,the dynamic equation of coupled vehicle-track systems under mixed coordinate was established by wheel-rail coupling characteristics.Base on the pseudo excitation method the track irregularity was regarded as the stationary random process which can be transformed as pseudo harmonic,also the high order sensitivity of random response was obtained.Then perturbation method was used to compute the random vibration responses of coupled vehicle-track systems with parameter uncertainties subjected to track irregularity.In the Numerical example the efficiency and computational accuracy are demonstrated by Monte Carlo Simulation approaches.
引文
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[2]Muscolino G,Benfratello S and Sidoti.A.Dynamics analysis of distributed parameter system subjected to a moving oscillator with random mass,velocity and acceleration[J].Probabilistic Engineering Mechanics,2002,17(1):63-72.
[3]Fryba L,Nakagiri S,Yoshikawa N.Stochastic finite elements for beam on a random foundation with uncertain damping under a moving force[J].Journal of Sound and Vibration,2003;163(1):31-45.
[4]Gladysz M,Sniady P.Spectral density of the bridge beam response with uncertain parameters under a random train of moving forces[J].Archives of Civil and Mechanical Engineering,2009,9(3):31-47.
[5]Wu S Q,Law S S.Dynamic analysis of bridge-vehicle system with uncertainties based on the finite element model[J].Probabilistic Engineering Mechanics,2010,25(4):425-432.
[6]Wu S Q,Law S S.Dynamic analysis of bridge with non-Gaussian uncertainties under a moving vehicle[J].Probabilistic Engineering Mechanics,2010,26(2):281-293.
[7]Lu F,Kennedy D,Williams F W,Lin J H.Symplectic analysis of vertical random vibration for coupled vehicle-track systems[J].Journal of Sound and Vibration,2008,317:236-249.
[8]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.(Lin J H,Zhang Y H.Pseudo Excitation Method in Random Vibration[M].Beijing:Science Press,2004.(in Chinese))
[9]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.(Chen G.Analysis of Random Vibration for Vehicle and Track Coupling System[D].Chengdu:Southwest Jiaotong University,2000.(in Chinese))