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

Abstract

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.

Vibration Analysis of Composite Laminated Plates Using Analytical and APDL ANSYS Codes

“…That is why the natural frequency increases as number of layers increases and consequently the natural frequency decreases as aspect ratio increases. The effect of aspect ratio (a/b) on natural frequency for cross ply clamped boundary condition as shown in Figure (11). It is observed that as increasing the aspect ratio, the natural frequency of two layers decreases about 45% less than of four layers.…”

Forced vibration analysis of composite beams with piezoelectric layers based on the variable separation method

“…reference. It should be mentioned here that for the cantilever and the clamped beam tests it is required to build simutaneously 2-tuple in order to achieve accurate results as in [54]. Further information on this technique can be also found in [55,56].…”

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

“…43 (b), that when the thickness ratio increases, it leads to a reduction in plate stiffness, which causes lower FV frequency values. Moreover, Vidal et al [364] employed the variable separation method (VSM) to investigate the FV of LCPs, and the FEM has been used for the in-plane description. Furthermore, Fantuzzi et al [365] performed a simulation analysis on LCPs with various geometries by utilizing the linear approach of moderately thick plates, and the strong form of FEM as well as WFm was used for solving the problem.…”