AN EFFICIENT HYBRID METHOD FOR DYNAMIC ANALYSIS OF TRAIN-TRACK-BRIDGE COUPLED SYSTEMS BASED ON THE MODAL SUPERPOSITION METHOD AND DIRECT STIFFNESS METHOD

To improve the computational efficiency for analyzing the vibration of train-track-bridge coupled systems (TTBSs), an improved hybrid method (IHM) is proposed by combining the direct stiffness method (DSM) and the modal superposition method (MSM) based on the hybrid method. The vibration equations of the train are established by applying multi-body dynamics. The vibration equations of the track are established by using the DSM, which can effectively display the local dynamic behavior with high frequency. The vibration equations of the bridge are established by using the MSM, a method that can efficiently reduce the degrees of freedom. The train and track are coupled as a train-track subsystem through the linear wheel-rail Hertz contact model. The train-track subsystem and the bridge subsystem are coupled by enforcing the compatibility of forces at the contact points between the track and the bridge. The proposed method is validated by the field measurement data collected from a 32 m simply supported girder bridge on the Shuo-Huang heavy-haul railway line. A numerical example of a CRH2 high speed train passing the Wan-Ning Bridge is provided to investigate the effects of the number of bridge modes on the accuracy of the dynamic responses. The computation time of the three different methods for analyzing the vibration of the TTBS is compared and the results show that the IHM has the most computational efficiency than the other two methods.