Three-dimensional elasticity solution of cross-ply shallow and non-shallow panels with piezoelectric sensors under dynamic load

Dynamic response of cross-ply laminated shallow and non-shallow panels with a piezoelectric layer is studied. Three-dimensional elasticity solution is presented for finitely long, simply-supported, orthotropic, shell panel under dynamic pressure excitation. The exact solution for non-shallow panels and an approximate method for shallow panel solution (Soong) are considered and compared with each other. 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. Numerical examples are presented for [0/90/P] lamination and the results of the shallow and non-shallow panels are discussed.