Dynamic Response Analysis of Vehicle–Bridge Coupled Systems of Low-to-Medium-Speed Maglev Long-Span Bridges

The vibration behavior of the maglev train–bridge system has consistently been a primary concern in developing low-to-medium-speed maglev transportation. In this study, based on the planned maglev train crossing the Xiangjiang River Bridge, the total vibration potential energy of the maglev train is extracted using a mathematical method. Following the principle of minimum total dynamic potential energy in elastic systems and the “set-in-right-position” rule, the equations of motion for the maglev train–bridge coupled system are established. The analytical framework and solution process of the coupling equation are developed using the pseudo-excitation method and evolutionary spectrum theory. The dynamic responses of the long-span continuous girder bridge, subjected to moving maglev trains, are analyzed through a Fortran program. The natural frequency and dynamic coefficient of the bridge structure are calculated, and the dynamic response parameters are obtained. Finally, the vibration comfort of the bridge is evaluated using the Diekemann and Sperling indices. The results indicate that the bridge vibration is within acceptable limits, demonstrating that the analyzed dynamic response parameters can serve as reliable references for the construction and design of magnetically suspended long-span continuous girder bridges, both in daily operation and management.