3D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported

On the basis of the three-dimensional theory of elasticity, a semi-analytical method, which combines the state space approach with the technique of differential quadrature, is developed for free vibration of a cross-ply laminated composite rectangular plate. The plate is assumed to be simply supported at one pair of opposite edges such that trigonometric functions expansion can be used to satisfy the boundary conditions precisely at these two edges. The technique of differential quadrature is then incorporated into the state equation, which enables one to obtain a general solution for orthotropic laminates with arbitrary boundary conditions at the other pair of opposite edges. The method is verified by comparing the present results with the exact elasticity solution for a simply supported plate. Further numerical calculations are carried out and effects of some parameters on natural frequency are discussed.