Free vibration analysis of composite plates based on a variable separation method

This work deals with the free vibration analysis of laminated composite plates through a variable separation approach. The displacement field is approximated as a sum of separated functions of the in-plane coordinates x, y and the transverse coordinate z. This choice yields to a non-linear problem that can be solved by an iterative process. That consists of solving a 2D and 1D eigenvalue problem successively. In the thickness direction, a fourth-order expansion in each layer is considered. For the in-plane description, classical Finite Element method is used. A wide range of numerical tests involving several representative laminated and sandwich plates is addressed to show the accuracy of the present LayerWise (LW) method. Different slenderness ratios and boundary conditions are also considered. By comparing with exact or 3D FEM solutions, it is shown that it can provide accurate results less costly than classical LW computations.