Finite-element analysis for a Timoshenko beam subjected to a moving mass

This article presents a finite-element formulation of a Timoshenko beam subjected to a moving mass. The beam is discretized into a number of simple elements with four degrees of freedom each. The inertial effects of the moving mass are incorporated into a finite-element model. The equation of motion in matrix form with time-dependent coefficients for a Timoshenko beam subjected to a moving mass is derived from the variational approach. The equation is solved by the direct step-by-step integration method to obtain the dynamic response of a Timoshenko beam and the contact force between the moving mass and the beam. The correctness of this present method is validated by means of comparison with the solution obtained by the assumed-mode method. The present method can be effectively used in computation for a Timoshenko beam with various boundary conditions. Numerical simulations are performed to demonstrate the efficiency of the present method.