Transient responses of Timoshenko beams subject to a moving mass

Abstract

The dynamic behavior of beam structures subject to a moving mass is a topic of practical importance in many research fields. In this study, the method of reverberation-ray matrix is presented to investigate the dynamic responses of an undamped Timoshenko beam subject to a moving mass. Based on Inglis’s assumption, the moving mass is simplified into a moving force and a concentrated mass fixed at the mid-span of the beam. Two dual local coordinates are introduced. Based on the theory of elastodynamics, the general wave solutions with two sets of unknown amplitude coefficients are derived in the transformed domain by the dual integral transform. From continuity conditions of forces and displacements at each joint and the compatibility conditions with respect to the dual coordinates, the unknown amplitude coefficients can be determined exactly. The transient dynamic motions for a Timoshenko beam under a moving mass are then determined numerically by inverse integral transform in which the Neumann series expansion is employed to avoid the integral singularities. Two simple numerical examples are presented and the results so obtained are compared with both the experimental and theoretical ones. It is shown that the present method can be a simple alternative for determining dynamic responses of bridges subject to a moving vehicle.