Rods with variable area cross-sections are structural components in many engineering structures. A study of the vibration characteristics in these structures is of great importance in designing the structures and in monitoring their performance as well. We present an application of a numerical method - the Pseudospectral (PS) method - to study the vibrations of an elastic rod of non uniform cross section material citing literature that shows recent interest in this area of study. One of the main advantages of the PS method is in its simplicity and ease of computation. The natural frequencies of the rod under varying end conditions are calculated. Results show good agreement with previous available analytical solutions. This work demonstrates the efficacy of the PS method in obtaining numerical solutions that are as good as exact solutions in practically used frequency ranges in the case of vibration problems of structural elements.

Keywords: Longitudinal, Vibration, Non-uniform, Rods, Pseudospectral method.