Free Vibration of Thick Quadrilateral Laminates Using Third-Order Shear-Normal Deformation Theory

Free vibrations of thick and skew quadrilateral laminates have been analyzed by using the Ritz method and a third-order shear and normal deformable plate theory (TSNDT) that does require a shear-correction factor. The weighted orthogonal Jacobi polynomials are employed as basis functions that exactly satisfy essential boundary conditions at the plate edges. An in-house-developed software is first verified by comparing computed frequencies with those either available in the literature or found by using the three-dimensional linear elasticity-theory-based finite-element-based commercial software ABAQUS. The method is applied first to find the lowest few (six in most examples) frequencies of isotropic cantilever plates of different skew angles and thickness-to-side length ratios. Subsequently, natural frequencies of laminated composite plates for various skew angles, thickness-to-side ratios, numbers of layers, and stacking sequences are compared with those obtained from converged solutions using either shell or brick elements in ABAQUS. It is demonstrated that the TSNDT/Ritz method provides highly accurate frequencies. Three-dimensional mode shapes are presented for a better understanding of the dynamic behavior of skew quadrilateral laminates.