Investigation of the Nonstationary Stochastic Response of Functionally Graded Piezoelectric Material Plates with General Boundary Conditions

Abstract

The functionally graded piezoelectric material (FGPM) has been widely used in various engineering cases due to its excellent mechanical properties. So far, the investigations on the stochastic dynamic behaviors of FGPM structures are few. This paper develops a unified solution for the nonstationary stochastic responses of the FGPM plate with general boundary conditions, in which the point, distributed and base acceleration random excitations can be considered. The first-order shear deformation theory (FSDT) is adopted to formulate the energy functional of the system and the governing equations are deduced by using the Hamilton's principle. The solutions of the system are obtained based on the modified Ritz method and pseudo excitation method (PEM). The accuracy of the proposed model is validated by comparing the obtained free vibration and random response results with those from the published literature. Finally, the effects of key parameters including boundary conditions, external electric voltage, material constituent and time modulated function on the stochastic response of the FGPM plate are investigated.