Application of the differential transformation method to vibration analysis of stepped beams with elastically constrained ends

The purpose of the present paper is to apply the differential transformation method (DTM) to deal with the vibration problem of stepped beams with general end supports and elastically constrained ends. The method demonstrates several advantages, such as rapid convergence, high accuracy, and computational stability. Unlike some approximate approaches which require correct assumed admissible function, the differential transformation method gives all natural frequencies and their mode shapes without any frequency missing. By using the DTM algorithms fully provided in this paper with general mathematical software packets, natural frequencies and mode shapes of these beams can be obtained easily for every boundary condition. Aspects such as boundary conditions, spring constant values, stepped beam types, step ratio and step location, which have a significant impact on frequencies and mode shapes, are taken into investigation in this paper.