Abstract
An analytical procedure to investigate the dynamic response of cross-ply laminated composite plates is presented. The solution is applicable to rectangular plates whose parallel edges are simply supported and the remaining ones can have arbitrary combinations of clamped, simply supported, and free-boundary conditions. A generalized modal approach is used to obtain these solutions. The equations of motion of the third-order, first-order, and classical theories are converted into a single-order system of equations by using state variables. The biorthogonality conditions of principal modes of the original and adjoint eigenfunctions are used to decouple the state space equation. The closed-form solutions developed are illustrated in a number of figures revealing the influences of the transverse shear deformation, of the degree of anisotropy, and of the character of boundary conditions on the response and the normal stress of the plate.