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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.

The vibrational characteristics of an infinite plate with structural inhomogeneities represented by a stiffness that varies periodically in space are considered. The plate properties and the forcing function selected all vary in the same direction so that the inhomogeneous plate equation reduces to the inhomogeneous beam equation. The coupled fluid-structure interaction problem then results in a linear ordinary differential equation with varying coefficients. This equation is then transformed into Fourier space and it results in a difference equation for the transformed plate displacement. The difference equation is then solved in the Fourier space for the distributed loading function, and the inverse of the transform of the plate displacement is then obtained. Typical results are presented. PACS numbers: 43.40.Dx FIG. 5. Plate displacement distribution; b --0.2, 0 --0.2. 2221