Dynamic Analysis Of Nonlinear Piezoelectric Laminated Axisymmetric Circular Plates

The topic of this paper is from piezoelectric smart structure models having practical applied background. Piezoelectric materials are electromechanical coupling materials extensively applied to fields of aerospace, high-precision and medical apparatus that need monitor and control on deformation. But the couplings of deflection and electric fields make it complicated to solve the math models representing physical problems considering nonlinearity. Hence, most of the studies on piezoelectric systems were based on linear geometric relations and linear piezoelectric effects. However, it's essential to investigate nonlinearity to reveal further characteristics of materials and nonlinear piezoelectric effects on strcutres. In this paper, static and dynamic behaviors of a piezoelectric laminated axisymmetric circular plate structure are studied with a view to influence of the geometric nonlinearity and nonlinear piezoelectric effects. The nonlinear control equations of PDFs are gained by the math model derived from mechanics and piezoelectricity. Because of double nonlinearity, the equations describing the problem are complicated and it's difficult to solve them. First, the nonlinear control equations of the unsymmetric ply laminated circular plates are simplified by adjusting the place of the coordinate axes. Next, the exact solutions of static control equations of the plates for simply supported and fixed supported boundary conditions are obtained by power series method. Then, Galerkin method and KBM perturbation method are used to solve the nonlinear dynamic control equations for simply supported condition. At last, by numerical calculation and analysis of bimorph and unimorph piezoelectric circular plates, the scope of electric field and mechanical force influencing displacement and axis force of the plates are found and the nonlinear relations...