Dynamic Analysis on Continuous Beam Carrying a Moving Mass with Variable Speed

Purpose: The excellent numerical behaviors of the structure-preserving method had been illustrated in the applications on the orbit-attitude-vibration space coupling dynamic problems. In this paper, the generalized multisymplectic method, a typical structure-preserving approach for the infinite-dimensional non-conservative systems, is employed to study the vehicle-bridge interaction problem. Method: Firstly, the coupling dynamic equation of the vehicle-bridge interaction system is presented, in which, the bridge is simplified as a multi-span continuous beam and the vehicle as a moving mass with a variable speed. Secondly, the dynamic symmetry breaking of the first-order matrix form of the dynamic equation is discussed under the framework of the generalized multi-symplectic theory. The Preissmann scheme of the first-order matrix form with the discrete condition that ensures the structure-preserving properties of the Preissmann scheme is constructed. Results and Conclusions: Referring to the discrete condition, the permitted positive/negative accelerations of the moving mass are obtained with different step length and different damping factor of the beam. By using the Preissmann scheme, the effects of the acceleration of the mass as well as the effects of the damping factor of the 3-span continuous beam are investigated in detail.