Vibrational characteristics of an infinite flat plate with varying properties

Abstract

A theory to study the vibrational characteristics of a structure with properties varying along its length is developed. The analysis consists of assuming that the plate thickness and plate stiffness are functions of the axial distance x. The resulting thin plate equation becomes a fourth-order differential equation with variable coefficients. The equation is solved by Fourier transform techniques and a solution in the transformed plane is obtained. The analysis is then applied to a constant thickness plate with sinusoidally varying stiffness. For simplicity, the effect of fluid loading is neglected and the forcing function is assumed to be given by a distributed load. Results in the form of plate displacement disribution are presented.