Dynamic Analysis of non-Prismatic Beam under non-Concentric Axial Force by using The Differential Transformation Method

Abstract

In this study, the dynamic analysis of non-prismatic simply-supported Euler-Bernoulli beam subjected to non-concentric compressive axial force has been presented. Kinetic and potential energy expressions of the model are derived. Hamilton’s principle is used to obtain the governing equations of motion. The fourth order differential equation with variable coefficient of the beam dynamics and buckling is solved using Differential Transform Method (DTM) to obtain mode shape, natural frequencies and buckling load of the system. The computer package Mathematical is used to write a program to calculate the natural frequencies, buckling load and the mode shapes. The effects of the taper ratio, eccentricity, and bucking load are investigated. The results are compared with the results of the analytical solution where a very good agreement is observed. The results show that the natural frequencies of prismatic and non-prismatic beam decreased when the compressive axial force increased. Also, the results show that when the taper ratio and eccentricity increased, the natural frequency of non-prismatic increases. The buckling load factor decreases when the taper ratio increases.