Efficient numerical approach to unbounded systems subjected to a moving load

Abstract

The present paper solves numerically the problem of vibrations of infinite structures under a moving load. A velocity formulation of the space-time finite element method was applied. In the case of simplex shaped space-time finite elements, the 'steady state' dynamic behaviour of the system was obtained. A properly performed discretization allowed of propagating information in a given direction at a limited velocity. The solutions were obtained under the assumption that the deformation is quasi-stationary, i.e., stationary in the coordinate system that moves with the load. The unbounded Timoshenko beam subjected to a distributed moving load was used as a test example. The dynamical system is placed on an elastic foundation. The matrices describing an infinite dynamical system subjected to a moving load are derived and the stability of the numerical scheme is analysed. The numerical results are compared with the analytical solutions in the literature and the classical numerical method.