Vibration of a circular beam with variable cross sections using differential transformation method

In this paper, an application of differential transformation method (DTM) is applied on free vibration analysis of Euler-Bernoulli beam. This beam has variable circular cross sections. Natural frequencies and corresponding mode shapes are obtained for three cases of cross section and boundary conditions. MATLAB program is used to solve the differential equation of the beam using DTM. Comparison of the obtained results with the previous solutions proves the accuracy and versatility of the presented problem.