A Study On Nonlinear Random Vibration Analysis Of Coupled Vehicle-Bridge Systems By An Explicit Time-Domain Method

With the rapid development of highways and high-speed railways in China,the problem of coupled vibration between the vehicle and bridge subsystems caused by deck or track irregularities has become more and more important for the vehicle running safety,the vehicle ride comfort,and the serviceability of the bridge.In addition,as the proportion of bridge mileage in the mileage of traffic lines increases,it is very probable that the train happened to be on the bridge when earthquakes occur,so it is necessary to further consider the impact of earthquakes in the problem of coupled vehicle-bridge vibration.Because deck or track irregularities and seismic excitations are random in nature,and coupled vehicle-bridge systems are also inherently time-varying,the problem of coupled vehicle-bridge vibration is a typical non-stationary random vibration problem.In the problem of coupled vehicle-bridge random vibration,scholars mainly focus on the research on linear coupled vehicle-bridge systems in the current works,and the research on problem of nonlinear coupled vehicle-bridge systems random vibration is still rare.This paper is devoted to the development of accurate and efficient methods for nonlinear random vibration analysis of coupled vehicle-bridge systems with nonlinear Hertz contact.On this basis,this method is further used to carry out researches on vehicle derailment safety and vehicle ride comfort evaluations,and the subsequent random vibration problem of large-scale complex coupled vehicle-bridge systems.The main work in this paper is described as follows:(1)The literature review on the problem of vehicle-bridge coupled vibration is carried out.Firstly,commonly used mechanical models of coupled vehicle-bridge systems and their advantages and disadvantages are introduced briefly.Secondly,deterministic vibration analysis methods and random vibration analysis methods of coupled vehicle-bridge systems are mainly emphasized,and their advantages and disadvantages are summarized.Finally,existing vehicle derailment safety evaluation indexes and vehicle ride comfort evaluation methods are summarized comprehensively.(2)The research on explicit time-domain method(ETDM)for random vibration analysis of coupled vehicle-bridge systems with nonlinear Hertz contact is developed.Considering two cases of deck irregularities only,and both deck irregularities and earthquakes,the explicit timedomain expressions for dynamic responses of the vehicle and bridge subsystems are first eatablished,respectively.By using the dimension-reduced explicit formulation of dynamic responses and considering nonlinear Hertz contact condition between the vehicle and bridge subsystems,an ETDM is proposed for fast nonlinear time-history analysis of coupled vehiclebridge systems,in which a dimension-reduced iteration scheme is conducted focusing on a small number of degrees of freedom assosiated with the wheel-rail contact points,leading to a significant reduced computational cost in the nonlinear analysis.On this basis,combined with Monte Carlo simulation(MCS)further,an efficient MCS based on ETDM with dimensionreduced iteration scheme is proposed for the nonlinear random vibration analysis of coupled vehicle-bridge systems with nonlinear Hertz contact.(3)The research on the engineering application of nonlinear random vibration of large-scale complex coupled vehicle-bridge systems is developed.Taking the Egongyan track bridge as the engineering application background,the efficient MCS based on ETDM with dimensionreduced iteration scheme is used to perform the nonlinear random vibration analysis of coupled vehicle-bridge systems under deck irregularities only,and under both deck irregularities and earthquakes.The accuracy and efficiency of the proposed method are verified through comparison with the traditional random simulation method.Finally,researches on vehicle derailment safety evaluation and vehicle ride comfort evaluation of a four-axis vehicle moving across the Egongyan track bridge are carried out.Research indicates that the proposed efficient MCS based on ETDM with dimension-reduced iteration scheme can effectively solve the problems of nonlinear random vibration analysis of coupled vehicle-bridge systems considering nonlinear Hertz contact,with good accuracy and high efficiency.The nonlinear random vibration analysis of a four-axis vehicle moving across the Egongyan track bridge is used to demonstrate the accuracy and efficiency of the proposed methods.