Analytical solutions for vibrations of laminated and sandwich plates using mixed theory

A semi-analytical method has been presented in this paper to evaluate the natural frequencies as well as displacement and stress eigenvectors for simply supported, cross-ply laminated and sandwich plates by using higher order mixed theory. Models based on equivalent single layer as well as layerwise (LW) theories have been formulated. By assuming a non-linear variation of axial displacements through the plate thickness, the warping of the transverse cross-section has been considered. Hamilton’s principle has been employed to derive the equilibrium equations. The proposed LW model fulfills a priori the continuity of displacements as well as the transverse and the normal stress components at each interface between two adjacent layers. Results obtained by present higher order mixed theory have been found in good agreement with those obtained by three-dimensional elasticity solutions. After establishing the accuracy of present results for orthotropic plates, new results for thin and thick sandwich plates have been presented which can serve as benchmark solutions for future investigations.