Vector Form Intrinsic Finite Element Method for Stochastic Analysis of Train-Track-Bridge Coupling System

In this paper, a train-Track-bridge (TTB) interaction model that can account for coach-coupler effect is presented for stochastic dynamic analysis of a train traveling over a bridge. Based on the vector form intrinsic finite element (VFIFE) method, both the bridge and non-ballasted track are discretized into a set of mass particles connected by massless beam elements, in which the fasteners that fixed the tracks on the bridge deck are modeled as a series of linear spring-dashpot units. The multi-body train car is regarded as seven mass particles (1 for car body, 2 for bogies and 4 for wheelsets) connected by parallel spring-dashpot units. Considering the random nature of rail irregularities, the Karhunen-Loéve expansion (KLE) method is used to simulate the vertical profile of the tracks. To calculate the mean and standard deviation of the stochastic response of the TTB system, the point estimated method (PEM) based on the Gaussian integration and dimension reduction method is adopted. The proposed VFIFE-TTB interaction model is then applied to stochastic resonance analyses of a train moving on a bridge. It is shown that the present VFIFE-TTB model is able to analyze the dynamic interaction of the TTB system simply and efficiently. The influence of rail irregularity-induced stochastic vibration on the train and bridge would become significant once the resonant vibration takes place on the TTB system.