Free vibration of antisymmetric angle-ply laminated plates including various boundary conditions

Abstract

A powerful analytical procedure to investigate the free vibration of antisymmetric angle-ply laminated plates is developed. The procedure, based on a generalized Lévy-type solution considered in conjunction with the state space concept, enables one to solve exactly the equations governing the laminated anisotropic plate theory as considered by Yang, Norris and Stavsky (YNS). The theory is a generalization of Mindlin's theory for isotropic plates to laminated anisotropic plates and includes shear deformation and rotary inertia effects. The solution is applicable to rectangular plates with two opposite edges simply supported and the remaining ones subjected to a combination of clamped, simply supported and free boundary conditions. The closed form solutions obtained are illustrated numerically in a number of figures and tales revealing the influences of the transverse shear deformation, of the degree of anisotropy, of the geometrical parameters of the plate, of the number of layers, of the ply-angles, and of the character of the boundary conditions. Comparisons with exact and finite element solutions (obtained for simply souppored edge conditions) are made and appropriate conclusions concerning the various effects are presented. © 1988, Academic Press Limited. All rights reserved.