Derivation of the Governing Differential Equation of Vibrating Host Plate with Two Piezoelectric Patches

Abstract

One of the most difficult challenges facing researchers these days is making industrial applications (e.g. engines, automobiles, and aircraft) run on renewable energy and reducing the use of fuel as much as possible. One approach to achieve this goal is the use of smart materials such as piezoelectric materials which produce mechanical stress or strain under the application of an electrical field. Vice versa, if this material is subjected to a mechanical strain, an electrical field will result. Piezoelectric materials are used as sensors or actuators for the structural control of smart structures. In this paper, a mathematical model represented by the governing differential equation for a host plate containing two piezoelectric patches has been developed to predict the displacement of a plate excited by the piezoelectric patches and transverse loads.