Nonlinear Frequency Responses of the Bistable Piezoelectric Plate

In the past few years, the energy harvester of piezoelectric beam has been extensively studied. In this paper, the bistable piezoelectric plate was adopted as the structure of energy harvester. The model consists of four parts including the substructure layer, the piezoelectric film, the protective layer and the magnet, which the material of the substructure layer and the piezoelectric layer are respectively carbon fiber and PVDF. The boundary conditions of the plate are simply supported by two opposite sides, which the other two sides are free. The base of the plate is subjected to the harmonic excitation. Based on von Karman large deformation theory and Hooke law, the partial differential equation for nonlinear vibration of the bistable piezoelectric system is derived by using Hamilton's principle. The Galerkin method is employed to discrete the partial differential equations to the ordinary differential equations. Then, the method of multiple scales is applied to perturbation analysis to obtain the nonlinear averaged equations in the polar form. Frequency-response curves of the piezoelectric plate are obtained by numerical simulations. The effects of the excitation amplitude, the damping coefficient, the piezoelectric parameters, the nonlinear parameters and the magnetic distance on nonlinear vibration of the bistable piezoelectric plate are studied.