Dynamic analysis of three-dimensional high-speed train-track model using moving element method

Abstract

In this article, the dynamic analysis of three-dimensional high-speed train-track model is carried out using moving element method. The train comprises a car-body supported by a secondary suspension system to a bogie. The bogie is in turn connected to wheel-sets through a primary suspension system. A total of 16 degrees of freedom is employed to describe the vertical, lateral, rolling, pitching, and yawing displacements of the car-body, the bogie, and the wheel-sets. The Hertzian contact and Kalker’s linear theory are used to account for the vertical and lateral contact forces between the wheels and rails. Two rails are modeled as two Euler–Bernoulli beams resting on a viscoelastic foundation. The moving element method is extended to establish the coupling formulations of the mass, damping, and stiffness matrices in vertical and lateral directions, where the element matrices are formulated based on a convected coordinate system attached to the moving vehicle. The dynamic amplification factor is defined as the ratio of the maximum dynamic contact force to the static load at the contact point between the wheel and the rail. To illustrate the benefits of the proposed three-dimensional train-track model, several numerical examples are performed in this study to present the effects of the train speed, the resonance phenomenon, the track irregularity, and track stiffness variations along the track and across the track width on the dynamic amplification factor of the high-speed train.