Static Bending and Vibration Analysis of a Rectangular Functionally Gradient Piezoelectric Plate on an Elastic Foundation

Abstract

In this paper, a functionally graded piezoelectric plate on an elastic foundation composed of two different piezoelectric materials bonded together in the form of plate is studied, and its static bending and fundamental frequencies are analyzed. First, based on Kirchhoff plate theory and the Hamilton principle, the governing equations and corresponding boundary conditions of the model are derived, and then the equations are discretized and solved by the differential quadrature method (DQM). Finally, the effects of physical parameters such as length-to-height ratio, length-to-width ratio, material graded index, foundation stiffness coefficient, temperature change value and external voltage value on static bending deflection, and fundamental frequency value of the functionally graded piezoelectric plate with four sides simply supported are discussed. The calculated results are in good agreement with those in the literature. The data results show that the increase in the elastic foundation stiffness coefficient will increase the equivalent stiffness of the plate. In the process of work, due to the equivalent pressure value generated by the influence of the external voltage, it will lead to unstable phenomena.