Analysis of Axially Vibrating Variable CrossSection Isotropic Rod Using DTM

Differential Transform Method (DTM) has a very wide applications in the field of structural vibration of various elements such as beams, plates, cylindrical shells and tanks. One of the most advantages of the DTM is its simple forms for nonlinear formulations. In this paper the free vibration of a general variable crosssection rod were studied. The nondimensional natural frequency and the normalized mode shapes of the nonuniform rod of free and clamped boundary conditions were obtained and compared with previous works. Results showed good agreement with the previous analytical solutions. The effect of the varying cross section area on the vibration are studied. This work reflects the power of the DTM in solving nonuniform problems.