Numerical Analysis of Free Longitudinal Vibration of Nonuniform Rods: Discrete Singular Convolution Approach

Abstract

In this paper, the problem of longitudinal free vibration of nonuniform rods is investigated for the first time by using the discrete singular convolution (DSC). This method is a relatively novel and powerful numerical approach especially in analyzing vibration problems. The governing equation of this problem is nonlinear and has analytical solutions only in a few cases, so the analysis uses DSC as a numerical method. The regularized Shannon delta kernel is used in the present algorithm. The nondimensional natural frequencies of rods with various-area cross sections have been studied in this paper. Results show good agreement with the previous analytical solutions. This study indicates the efficiency of the DSC in solving nonuniform rod problems.