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

  • Talib H. Elaikh Mech. Eng. Depart., College of Engineering,University of Thi-Qar
Keywords: Non-prismatic Euler-Bernoulli Beam, Non-concentric force, Hamilton’s Principle, le, Differential Transform Method


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