Study On Efficient Random Vibration Computational Method For Train-bridge System

With the rapid development of high-speed railway,the problem of vehicle-bridge coupled vibration has attracted considerable attention in the past few decades.Track irregularity is the main excitation source for the vehicle-bridge system,which is usually regarded as deterministic excitation in early research to simplify the analysis.In fact,track irregularity is essentially a random process,so it is more reasonable to study the vehicle-bridge interaction problem using the random vibration theory.There are some methods suitable for random vibration analysis(RVA)of vehicle-bridge system in the literature,but these methods generally require a large number of time-frequency integrations or repeated time-history analysis,which is very timeconsuming in practical application.Aiming at the the development of efficient RVA methods for the vehicle-bridge system,the following work is carried out in this thesis:(1)For the problem of non-stationary random vibration of bridge under train loads,the wheel-rail force is simulated as a stationary correlated random process with time delay,and the internal relationship between wheel-rail force and track irregularity processes is established using the frequency-domain random vibration theory.Next,a non-stationary RVA method based on spectral decomposition and modal superposition is developed to efficiently evaluate the timeand frequency-domain response statistics of bridge.The computational accuracy and efficiency of proposed method are verified by evolutionary spectral method and Monte Carlo simulation(MCS).In the numerical example,the effects of parameters of vehicle model and velocity of wheel-rail force on the random response of bridge are studied.(2)Taking the vertical vehicle-bridge coupled model excited by track irregularity as the research object,a spectral decomposition-based explicit integration method(SD-EIM)is proposed for the random vibration problem of time-varying system.This method derives the explicit expression between the responses of vehicle-bridge system and a set of orthogonal random variables,which can be used to effectively evaluate the time-frequency response statistics of the system.Compared with the traditional non-stationary RVA method that requires a large number of numerical integration or time-history analysis,SD-EIM only needs to evaluate the coefficient matrix of explicit response expression at discrete time points in a recursive manner,which is very convenient and efficient for numerical application.In the numerical example,the pseudo-excitation method and explicit time-domain method will be used to validate the accuracy and efficiency of the proposed method.(3)The non-stationary random vibration problem of three-dimensional train-bridge system(TBS)is further studied.Firstly,the multi-body dynamics theory and finite element method are used to establish the spatial motion equations of train and bridge,which are then coupled using the wheel-rail “no separation” hypothesis.Next,the SD-EIM is extended to the nonstationary RVA of three-dimensional TBS,the detailed formula derivation and computational process are given,the effects of vehicle speed,track level and other factors on the response characteristics of bridges and trains are studied.(4)Taking the vertical TBS model considering nonlinear Hertz wheel-rail contact as the research object,it is studied that how to realize the efficient evaluation of MCS response samples,so as to improve the computational efficiency of nonlinear RVA of TBS.Firstly,a wheel-rail force prediction method based on polynomial interpolation is proposed to accelerate the convergence of wheel-rail forces,based on which the calculation efficiency of single response sample in the traditional separation-iteration method can be improved.Next,a synchronous integration strategy is constructed to directly embeds the solution of multiple response samples into the iterative integration of TBS dynamic equation,avoiding the outer iteration of MCS and significantly improving the computational efficiency of a large number of response samples.Finally,an adaptive sampling method is constructed to reasonably determine the number of samples required in the evaluation of TBS response statistics.(5)The nonlinear random vibration of large-scale three-dimensional TBS is further studied.A three-dimensional nonlinear wheel-rail force model considering Hertz vertical contact and Kalker creep force is established to realize the coupling of spatial motion equations of train and bridge.Next,the prediction-iteration method mentioned above is extended to the nonlinear RVA of three-dimensional TBS,and the detailed computational flow is given.The vehicle-induced random vibration of a long-span cable-stayed bridge is considered in the numerical example,and the linear and nonlinear response characteristics of TBS are compared to analyze the influence of wheel rail contact model on the random vibration of vehicle-bridge system.