Vibration of Nonuniform Beams Under Moving Point Loads: An Approximate Analytical Solution in Time Domain

The forced-free responses of nonuniform beams under moving point loads are analyzed in this paper. Simple approximate analytical formulae for the forced responses of undamped nonuniform beams, derived using the fundamental mode by the Rayleigh–Ritz (R–R) method, are presented. The responses of both simply supported and clamped–clamped beams are analyzed. The responses are also determined by the finite element method (FEM) in which nonuniform elements are used for fast convergence. It is found that the present method yields results that are very close to those obtained by the FEM. As this method does not require time integration, it is faster and computationally more efficient. Though the single-mode analysis of forced vibration of uniform beams under moving loads has been done by several researchers, its application to nonuniform beams has not been reported.