Nonlinear vibration of a cantilever FGM rectangular plate with piezoelectric layers based on third-order plate theory

This paper deals with nonlinear dynamic analysis of a cantilever FGM rectangular plate with piezoelectric layers subjected to the transversal excitation in thermo-electro-mechanical environment. The material properties of plate and piezoelectric layers are assumed to be temperature-dependent. The governing equations of the functionally graded plate are based on the Reddy's third-order shear deformation plate theory that includes thermo-piezoelectric effects and Hamilton's principle. The governing nonlinear partial differential equations are transformed into ordinary nonlinear differential equations using the Galerkin method and the nonlinear and linear frequencies obtained using the Runge-Kutta method. The effects played by control voltage and system initial conditions on the nonlinear vibration of the plate are studied.