Forced Vibration Analysis of Non-Uniform Piezoelectric Rod by Complementary Functions Method

Abstract

Piezoelectric materials, which have fast response and low energy usage features, are widely used in sensors and actuators. Due to the active role of their working principle, it is important to know the vibration characteristic of each piezoelectric material. In this paper, forced vibration analysis of arbitrary non-uniform piezoelectric rod has been performed. The governing differential equations have variable coefficients which are functions of mechanical and electrostatic properties. Analytical solution of these linear differential equations is limited to specific cross-section area models, so numerical method is inevitable. Numerical model of the forced vibration of cantilever piezoelectric (PZT-4) rod with an arbitrary non-uniform cross-section area is obtained in the Laplace space and then solved numerically by Complementary Functions Method (CFM). Solutions were transformed from Laplace domain to the time domain by applying modified Durbin’s procedure. The technique is validated for a uniform piezoelectric rod that can also be solved analytically. In order to demonstrate the effect of arbitrary geometry on the dynamic feature of the rod, numerical examples are employed.