On The Dynamic Analysis of Non-Uniform Beams Under Uniformly Distributed Moving Loads

Abstract

In this paper, the dynamic response of a non-uniform beam subjected to uniformly distributed moving load is investigated. Specifically, the elastic properties of the beam, the flexural rigidity, and the mass density per unit length which are assumed constants are hereby expressed as functions of the spatial variable x. This dynamic response of the beam was analyzed using the finite element technique. Firstly, the non-uniform continuous beam was replaced by a non-continuous (discrete) system made up of beam elements. The modified elemental and overall stiffness, and mass matrices, the elemental and overall centripetal acceleration matrices as well as the load vector were derived. Next, the Newmark’s direct integration method was used to obtain the desired response of the beam. The major points of interest in this study were (i) the effect of velocity of the moving load (ii) the effect of load’s length, and (iii) the effect of the span length of the beam.