Free vibration of thick, layered rectangular plates by a finite layer method

Abstract

A three-dimensional linear, small deformation solution for the free vibration of thick, layered rectangular plates with various boundary conditions is developed using a finite layer method which is an extension of the well-known finite element method. In this method, the plate is divided into a number of layers, and the stiffness matrix of a layer element is obtained by assuming the displacement functions, u, ν and w to be of the form X( x) Y( y) Z( z), in which X( x) and Y( y) are suitable beam function series satisfying the appropriate boundary conditions of the plate, and Z( z) is a simple linear polynomial. A consistent mass matrix is also formed for each layer. The stiffness and mass matrices of all the layers forming a plate are then assembled to give an eigenvalue matrix which can be solved for the frequencies and the mode shapes on an intermediate size computer. The method is simple but versatile, and complex problems involving anisotropic materials or thick layered construction can all be handled easily.