A reduced time-varying model for a long beam on elastic foundation under moving loads

Dynamics of a long beam on the elastic foundation subjected to moving loads is studied in the present paper. The sliding window technique is used to dynamically truncate the long beam and a reduced time-varying beam system is obtained. The Hamilton’s principle is employed to establish the equations of motion of the reduced system. The variable separation method is adopted to solve dynamical responses of the reduced system. Examples of a long simply supported Timoshenko beam on the nonlinear foundation subjected to a single moving load and multiple loads are included. Numerical results of the reduced model compared with the ones obtained from the moving element model adapted in literature are carried out to show the validity and the good efficiency of the method proposed in the present paper.