Vibration analysis of cross-ply laminated square plates with general boundary conditions

This study is concerned with the vibration analysis of cross-ply laminated square plates subjected to different sets of boundary conditions. The analysis is based on a five-degree-of-freedom shear deformable plate theory. The requirement of the continuity conditions among the layers for the symmetric cross-ply laminated plates are fulfilled by the use of the shape functions incorporated into this theory which, also, unifies the two-dimensional shear deformable plate theories developed previously. Initially, the governing equations obtained by use of Hamiltonʹs principle for the vibration of cross-ply laminated plates with simply supported boundary conditions at all of their edges are solved by an exact analytical method. In the case of cross-ply laminated square plates subjected to twelve different combinations of free, clamped and simply supported edge boundary conditions, the free vibration frequencies are obtained by applying the Ritz method where the five displacement components are assummed as the series of simple algebraic polynomials. The numerical results obtained for different length-to-thickness ratios and material arrangements are presented and compared with the ones available in the literature.