The analysis of functionally graded shallow and non-shallow shell panels with piezoelectric layers under dynamic load and electrostatic excitation based on elasticity

Elasticity solution is presented for finitely long, simply-supported, functionally graded shallow and non-shallow shell panel with two piezoelectric layers under pressure and electrostatic excitation. The functionally graded panel is assumed to be made of many sub panels. Each sub panel is considered as an isotropic layer. Material’s properties in each layer are constant and functionally graded properties are resulted by suitable arrangement of layers in multilayer panel. In each interface between two layers, stress and displacement continuities are satisfied. The highly coupled partial differential equations (p.d.e.) are reduced to ordinary differential equations (o.d.e.) with variable coefficients for non-shallow panel and constant coefficients for shallow shell panel by means of trigonometric function expansion in circumferential and longitudinal directions. The resulting ordinary differential equations are solved by Galerkin finite element method and Newmark method is used to march in time. Numerical examples are presented for functionally graded shell panel with a piezoelectric layer as an actuator in external surface and a piezoelectric layer as a sensor in internal surface and the results of the shallow and non-shallow panels are discussed.