Research On The Property Of Nonlinear Static And Dynamic Mechanics Of Piezoelectric Rectangular Plate

First, an extensively survey of history, developing and status in quo of nonlinear static and dynamic mechanics of piezoelectric plates is presented. Through comprehensive studying, a mix model of higher order shear displacement, discrete higher order electric field, which is capable of capturing the actual distributions of the displacement and electric field of piezoelectric plate, is established. By applying the von Karman nonlinear strain theory and using Hamilton's variational principle, a coupling nonlinear control equations and edge conditions of piezoelectric lamina plate are derived. The nonlinear theory can represent the essence of the nonlinear mechanics of piezoelectric plate entirely and impersonally, and may decouple the nonlinearity efficiently as well. Hence, make a convenience for the analysis solution.Base on the characteristics of the operators of the nonlinear equations of piezoelectric plates and the edge conditions, using the Galerkin-double Fourier methods, the double Fourier-orthogonal function deploying methods, two solving procedure of the nonlinear equations of piezoelectric plate are derived. These two solving procedure and the nonlinear theory of piezoelectric plate derived are applied to the nonlinear bending problem of orthotropic plate and isotropic plate, the results are compared to those published results, it shows that these solving procedure are exactly and effectively.By the two solving procedures and the multiple scale method, the exact analysis solutions of nonlinear bending problems, post buckling problems, electric post buckling problems, nonlinear free vibration problems, nonlinear force vibration problems and buckling force vibration problems of singular layer piezoelectric plate (sensor and actuator) under transverse load and electric load are obtained.Numeric result shows that, the lager the synthetic elastic parameter,...