Higher Order Refined Computational Models for the Free Vibration Analysis of Antisymmetric Angle Ply Plates

Analytical formulations using two higher order refined displacement models have been developed and solutions presented for the first time to the natural frequency analysis of antisymmetric angle-ply composite and sandwich plates. These computational models already reported in the literature are based on Taylor's series expansion of the displacements in the thickness coordinate and consider the realistic parabolic distribution of transverse shear strains through the laminate thickness. One of them, with 12 degrees of freedom, considers the effects of both transverse shear and normal strain/stress while the other with 9 degrees of freedom includes only the effect of transverse shear deformation. In addition to above, a few higher order models and the first order model developed by other investigators and available in the literature are also considered for the evaluation. A simply supported plate is considered throughout as a test problem. The equations of motion are obtained using Hamilton's principle. Solutions are obtained in closed form using Navier's technique by solving the eigenvalue equation. Plates with varying slenderness ratios, number of layers, fiber orientations, degrees of anisotropy, edge ratios and thickness of core to thickness of face sheet ratios are considered for the analysis. Accuracy of the theoretical formulations and the solution method is first ascertained by comparing the results with those already available in the literature. After establishing the accuracy of the solutions, extensive numerical results are presented for the free vibration analysis of multilayer antisymmetric angle-ply composite and sandwich plates using all the models, which will serve as a benchmark for future investigations.