Analysis of general elastically end restrained non-uniform beams using differential transform

Abstract

This study introduces using differential transform to solve the free and forced vibration problems of a general elastically end restrained non-uniform beam, resting on a non-homogeneous elastic foundation and subjected to axial tensile and transverse forces. First, differential transform is briefly introduced. Second, taking differential transform of non-uniform beam vibration problems, a set of difference equations is derived. Doing some simple algebraic operations on these equations, we can determine any ith natural frequency, the closed form series solution of any ith mode shape and the dynamic response. Finally, two vibration problems are given to illustrate the accuracy and efficiency of the present method.