A Comparison of Closed-Form and Finite-Element Solutions for the Free Vibration of Hybrid Cross-Ply Laminated Plates

Abstract

The natural frequencies of hybrid cross-ply laminated plates are predicted using a high-order shear deformation theory and the three-dimensional finite-element analysis. The equations of motion for simply supported laminated hybrid rectangular plates are derived using the Hamilton principle. Closed-form solutions for antisymmetric cross-ply and angle-ply laminates are found employing the Navier solution. In the finite-element method, eight-node linear interpolation brick elements are used to model the composite plates. First, the analytical and numerical results are validated for an antisymmetric cross-ply square laminate by results available in the literature. Then, the effects of side-to-thickness ratio, aspect ratio, lamination schemes, and material properties on the fundamental frequencies for simply supported carbon/glass hybrid composite plates are investigated. Since no data are available in the literature for hybrid composite plates, the finite-element solution is used for comparison purposes. A comparison of the analytical solution with the corresponding 3D finite-element simulations shows a good accuracy of the proposed analytical solution in predicting the fundamental frequencies of hybrid cross-ply laminated plates.