Influence of the edge-boundary conditions on three-dimensional free vibrations of isotropic and cross-ply multilayered rectangular plates

This paper analyses the influence of different sets of edge-boundary conditions on the dynamics of freely vibrating isotropic and cross-ply multilayer laminated rectangular plates. The analysis is carried out within the frame of the full three-dimensional theory of elasticity through a formulation which is based on assumed displacements only; this formulation presents its relevant objectives in a unified manner, regardless of the nature of the stacking patterns of the laminated plates (isotropic, single layers or multi-layers). The analytical and/or numerical performance of the formulation is compared to those few results achievable through the exact three-dimensional theory and/or to those few existing results achieved by other researchers through alternative formulations. Convergence analyses are carried out on eigenvalues, displacement and stress fields in order to describe the capability of the formulation when compared to the exact three-dimensional results. The analysis reveals an interesting dependence on the edge-boundary conditions and highlights the need to carry out deeper investigations even though certain classical boundary conditions are taken into account through the most modern electronic computers.