Nonlinear vibration of transversely isotropic piezoelectric rectangular plate

Piezoelectric elements integrated with conventional elastic structure used as either sensor or actuator for structural identification and control play key roles as active components in smart structure system. Thus, a comprehensive and thorough understanding of nonlinear behaviors of piezoelectric structures is urgently required for engineering application. To broaden the theoretical fundamental of piezoelectric structures, the geometrically nonlinear relation between strain and displacement of a transversely isotropic piezoelectric rectangular plate is proposed and basic large deformation equations are established. General nonlinear vibration equations of transversely isotropic piezoelectric rectangular plate are formulated using Hamilton's principle. General electric and mechanical boundary conditions are derived. By applying the double Fourier series as the displacement mode and performing the Galerkin procedure, the exact solution of the free vibration of transversely isotropic piezoelectric rectangular plates is obtained under simply supported boundary conditions. The effects of parameters of the material and geometry on the characteristics of the vibrations are analyzed.