A three-dimensional free vibration analysis of cross-ply laminated rectangular plates with clamped edges

On the basis of three-dimensional elasticity, this paper presents a free vibration analysis of cross-ply laminated rectangular plates with clamped boundaries. The analysis is based on a recursive solution suitable for three-dimensional vibration analysis of simply supported plates. Clamped boundary conditions are imposed by suppressing the edge displacements of a number of planes which are parallel to the mid-plane. This is achieved by coupling a number of different vibration modes of the corresponding simply supported plate using a Lagrange multiplier method. A satisfactory solution can be obtained by choosing suitably larger numbers of the coupled vibration modes and the fixed planes across the thickness of the plate. Numerical results are presented to show the convergence of the solution. Results are also obtained for either isotropic or cross-ply laminated plates having different combinations of simply supported and clamped boundaries.