A Practical Method for the Dynamic Analysis of Non-Uniform Piezoelectric Rod

Abstract

In this paper, a unified approach for the dynamic analysis of non-uniform piezoelectric rod is presented. It is assumed that the cross sectional area of the rod is varying along the longitudinal axis, arbitrarily. Therefore, the partial differential equations that govern the non-uniform piezoelectric isotropic rod in a forced vibration analysis are obtained with a variable coefficient taking into account mechanical and electrostatic equations. Analytical solutions of these equations are only possible for simple cross- section areas. First, the governing equations are transformed to the Laplace space and then solved numerically by pseudospectral Chebyshev approach for arbitrary cross-section area under four different load functions. The final results are transformed to the time domain using modified Durbin’s procedure. The technique is validated for simple cross-section area results that can also be solved analytically.