Vibration of laminated composite plates using various plate theories: Analytical and finite element results

Analytical and finite element solutions of the classical, first-order, and third-order laminate theories are developed to study free vibrations of cross-ply rectangular composite laminates under various boundary conditions. The analytical solutions are developed using the space-state approach. The effects of side to thickness ratio, aspect ratio, and lamination schemes on the fundamental frequencies are investigated for the theories. The Levy type solution procedure and finite element model developed was used to evaluate the natural frequencies of antisymmetric, cross-ply, rectangular laminates. The effect of orthotropy and number of layers on the non-dimensional fundamental frequency of simply supported square laminates is investigated, and the numerical results obtained using various plate theories are compared. The fundamental frequencies increase with increasing orthotropy as well as the number of layers. In all cases, the classical plate theory over-predicts the frequencies compared to the shear deformation theories.