Nonlinear electro-thermo-mechanical dynamic behaviors of a supersonic functionally graded piezoelectric plate with general boundary conditions

A unified analytical model is developed to investigate the nonlinear aeroelastic behaviors of a supersonic functionally graded piezoelectric material (FGPM) plate with general boundary conditions under electro-thermo-mechanical loads. The formulation is derived by first-order shear deformation theory (FSDT) and supersonic piston theory, and the geometrical nonlinearity is considered based on von Karman large deformation theory. The motion equations of the supersonic FGPM plate are obtained through Hamilton principle and a modified Fourier series with auxiliary functions is employed to satisfy the possible mechanical and electric boundary conditions. Nonlinear aeroelastic responses of the FGPM plate are solved via Newmark integration technique combined with Newton-Raphson iterative scheme. Convergence and comparison studies show that the proposed model has sufficient accuracy in predicting aeroelastic stability and nonlinear dynamic responses as well as possess reliability in handling arbitrary boundary conditions. Numerical examples are carried out to demonstrate that several key parameters can significantly affect flutter and thermal buckling of the plate. Additionally, the effects of thermal and electric loads on limit cycle oscillation and dynamic bifurcation of nonlinear FGPM plate are examined. A higher temperature rise can result in the transition of the system from stable to chaos and more complicated evolution of dynamic motions.