Dynamic Response of a Nonuniform Timoshenko Beam with Elastic Supports, Subjected to a Moving Spring-Mass System

This paper is concerned with the dynamic response of a nonuniform Timoshenko beam with elastic supports subjected to a moving spring-mass system. The modal orthogonality of nonuniform Timoshenko beams and the corresponding overall matrix of undetermined coefficients are derived. Then the natural frequencies and mode shapes of nonuniform Timoshenko beams are obtained by the Runge–Kutta method and cubic spline interpolation method. By using the Newmark-[Formula: see text] method and the mode summation method, the vibration equation of Timoshenko beams subjected to a moving spring-mass system was established. A comparison of results between the proposed method and finite element method reveals that this method possesses favorable accuracy for dynamic response analysis. In numerical examples, the effects of the support spring and moving spring-mass system on Timoshenko beams have been examined in detail.