Nonlinear vibration analysis of piezo-thermo-electrically actuated functionally graded circular plates

A theoretical model for geometrically nonlinear vibration analysis of thermo-piezoelectrically actuated circular plates made of functionally grade material (FGM) is presented based on Kirchhoff's-Love hypothesis with von-Karman type geometrical large nonlinear deformations. The material properties of the FG core plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents. Dynamic equations and boundary conditions including thermal, elastic and piezoelectric couplings are formulated and solutions are derived. An exact series expansion method combined with perturbation approach is used to model the nonlinear thermo-electro-mechanical vibration behavior of the structure. Control of the FG plate's nonlinear deflections and natural frequencies using high control voltages is studied and their nonlinear effects are evaluated. Numerical results for FG plates with various mixtures of ceramic and metal are presented in dimensionless forms. A parametric study is also undertaken to highlight the effects of the thermal environment, applied actuator voltage and material composition of the FG core plate on the nonlinear vibration characteristics of the composite structure.