Research On Stochastic Vibration For Vehicle-Track-Bridge System Based On Probability Density Evolution Method

At present,research on the stochastic vibration of vehicle-bridge(VB)systems has attracted wide attention in the railway field.However,the existing research usually ignores the influence of the track structure.The dynamic parameters of the track structure have large randomness.The random non-uniformity of the longitudinal elastic stiffness of the track structure will cause elastic irregularity or dynamic irregularity on the top surface of the rail,and the local random damage in the track structure will cause short-wave dynamic irregularity on the top surface of the rail.From this point of view,it is obviously important to investigate the random effects of the track structure.In this paper,considering the track structure and its randomness,research on the stochastic vibration of the vehicle-track-bridge(VTB)systems are carried out based on the probability density evolution method(PDEM)from the following aspects.(1)In terms of the stochastic characteristics of the track structure,the random parameters are reasonably selected,and the stochastic motion equation of the VTB systems is derived based on the generalized energy principle.(2)In terms of the local vibration characteristics of the rail and the requirement of high-precision analysis,the rail is simulated by the high-precision element,and the stochastic motion equation of the VTB systems is derived based on the generalized energy principle.(3)In terms of the randomness of VTB systems parameters and track irregularity load,a stochastic vibration analysis method for VTB systems is proposed based on the probability density evolution method and the number theory method.(4)In terms of the high computational consumption caused by constant step size and constant interval in the process of probability density differential solution,a differential solving technique with adaptive step and interval is developed.Taking a typical multispan simply supported railway bridge as an example,the stochastic vibration characteristics of the VTB systems are systematically analyzed based on the theoretical research mentioned above for three types of random factors,i.e.,track random irregularity,random damages and random system parameters.The results indicate that the efficiency of the PDEM is significantly improved by employing the differential solving technique with adaptive step and interval in the stochastic vibration analyses of the VTB systems.The accuracy of the dynamic analyses of the VTB systems is effectively improved by the high precision VTB element,especially for the vehicle with high speed.The stochastic characteristics of the dynamic responses of the rail and bridge induced by the track random irregularity are significantly affected by the deterministic local damages existing in the track structure,which will be further amplified with the increase of the vehicle speed at the damage point of the track structure.The dynamic responses of the vehicle,rail,bridge and wheel-rail force are obviously induced by the random damages in the track structure,the random parameters in the track structure and the track elastic irregularity,and the random influences induced by the track elastic irregularity increase with the increase of the variation level of the wavelength of sine wave and the vehicle speed linearly.It is also non-negligible that the random effects induced by the random damages in the bridge structure,the random parameters in the bridge structure and the random parameters in vehicle.