Abstract
The geometrically nonlinear free vibration of symmetrically laminated rectangular plates (1st and higher modes) and the higher mode of an isotropic plate with fully clamped boundary conditions is studied, using the hierarchical finite element method (HFEM). The relationships between the vibration amplitude ratio and nonlinear frequencies, and between the vibration amplitude ratio and nonlinear mode shapes are discussed. The mode bending stresses and membrane forces at large amplitude for laminated plates are presented. The comparison between the nonlinear frequency ratio calculated from this study and the one from a published paper is in good agreement. The large variation of in-plane membrane forces over the plate span for some of the laminated plates has been observed. This will definitely affect the application of Berger's hypothesis to the geometrically nonlinear analysis of these laminated plates. It has been found that the geometrically nonlinear dynamic properties of laminated plates varies from plate to plate depending not only on the aspect ratio and boundary conditions, but also on the lamination and material properties of the lamina considered.
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