Coupling Vibration of Simply-Supported Damping Beam Carrying a Moving Mass

The coupling dynamic problems, such as the vehicle-bridge interaction problem, are difficult to be analyzed. In this paper, the generalized multi-symplectic approach is employed to investigate the coupling dynamic behaviors in the vehicle-bridge interaction system. A simply-supported damping beam model carrying a moving mass is considered and the generalized multi-symplectic form with the dynamical symmetry breaking factors is deduced firstly. And then, Preissmann’s scheme is employed to discretize the generalized multi-symplectic form, and the discrete structure-preserving condition for the numerical scheme is presented. According to the discrete structure-preserving condition, the permitted moving speed of the mass with different damping factors and different time step lengths is obtained to ensure the structure-preserving properties of the numerical scheme. Finally, the effects of the damping factor of the beam and the moving speed of the mass on the vibration of the beam are investigated by Preissmann’s scheme. The main contribution of this work is to provide a structure-preserving analysis approach for the vehicle-bridge interaction problem.