A Hybrid Method for Vehicle–Track Coupling Dynamics by Analytical and Finite Element Combination Technique

Globally, rail transit is developing toward higher speeds, larger axle weights, and greater environmental friendliness. The more and more complex wheel–rail interaction will result in the dynamic responses of vehicles, tracks and other structures needing more in-depth theoretical research. However, most existing models for dynamic simulations of the vehicle–track coupling system need to extend the model on both sides of the concerned region to eliminate the boundary effect. To a certain extent, this kind of process method increases the computational effort. To overcome this disadvantage, a hybrid model combined with the analytical method and finite element method was proposed. The moving support system (including transition nodes) was specially established referring to the analytical solution of rail deflection based on the Winkler elastic foundation beam theory to realize the combination of the two methods. Two examples were presented to verify the stability and accuracy of the proposed model. The comparison results show that simulation results of vertical wheel–rail forces and track vibrations are almost consistent with the existing model. Furthermore, the calculation efficiency was discussed and certificated under different long-marshalling trains, with an obvious speedup factor that could be more than 2.5 for 16-marshalling train. The proposed model has a wide application prospect in the vehicle–track coupling analysis of long-marshalling trains, especially for heavy haul railways with hundreds of vehicles.