Vibration of non-uniform rod using Differential Transform Method

The present paper analyses the vibration characteristics of non-uniform rods using Differential Transform Method. The method is very effective in solving ordinary and partial differential equations. The governing equations are transformed into a set of polynomials and the solution of these algebraic equations gives the desired frequency. Method is implemented for fix-free and fix-fix end conditions of a non-uniform rod. It is seen that the lower modes are sensitive to taper ratio in case of fix-free rod and fix-fix case frequency is same as that of uniform rod for different taper ratios. The method has proved to be accurate, simple and effective for eigenvalue analysis.