RMVT- and PVD-Based Finite Layer Methods for the Quasi-3D Free Vibration Analysis of Multilayered Composite and FGM Plates

摘要

The Reissner mixed variational theorem (RMVT)- and principle of virtual displacements (PVD)-based finite layer methods (FLMs) are developed for the quasi-three-dimensional (3D) free vibration analysis of simply-supported, multi-layered composite and functionally graded material (FGM) plates. The material properties of the FGM layers are assumed to obey either an exponent-law exponentially varied with the thickness coordinate or the power-law distributions of the volume fractions of the constituents. In these formulations, the plate is divided into a number of finite layers, where the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the field variables of each individual layer, respectively. Because an h- rather than p-refinement process is adopted to yield the convergent solutions in this analysis, a layerwise linear or parabolic function distribution through the thickness coordinate is assumed for the related field variables. The unified formulations of these two kinds of FLMs with freely-chosen orders are presented, which are used for expansion of in- and out-of-plane field variables through the thickness coordinate. The natural frequencies and their corresponding modal field variable distributions through the thickness coordinate of the multilayered composite and FGM plates are studied using the various RMVT- and PVD-based FLMs developed in this paper, and the accuracy and convergence rate of these are assessed by comparing their solutions with the exact 3D solutions available in the literature.