Effect of Mass per Unit Length on freely vibrating Simply Supported Rayleigh Beam

Abstract

In this paper, free vibration characteristics of a uniform Rayleigh beam are studied using the differential transform method. The procedure entails transforming the partial differential equation governing the motion of the beam under consideration and the associated boundary conditions. The transformation yields a set of difference equations. Some simple algebraic operations are performed on the resulting difference equations to determine any ith natural frequency and the closed-form series function for any ith mode shape. Finally, one problem is presented to illustrate the implementation of the present method and analyse the effect of mass per length on the natural frequencies of the beam.