Dynamic analysis of the train and slab track coupling system with finite elements in a moving frame of reference

Slab tracks are widely used worldwide in high-speed railways. In order to investigate the dynamic behavior of the train and slab track coupling system, a new approach, based on conceptions of the vehicle element and track element, is developed with finite elements in a moving frame of reference. By discretizing the slab track subsystem into track elements that flow with the moving vehicle, the proposed method eliminates the need for keeping track of the vehicle position with respect to the track model. The governing equations are formulated in a coordinate system traveling at a constant velocity, and the associated stiffness matrix, mass matrix and damping matrix for the track element in a moving frame of reference are derived. The vehicle element is introduced to model a car with primary and secondary suspension systems, which has 26 degrees of freedom, where 10 degrees of freedom are used to describe the vertical movement of the car, and 16 degrees of freedom are associated with the rail displacements. In the numerical study, four cases of application examples are presented taking into consideration the effects of track roughness, train speed and track parameters. The numerical solutions compare favorably with the results obtained by alternative methods. The method is shown to work for varying train speed and track parameters, and has several advantages over the conventional finite element method in a fixed system of reference.