Vibration of Functionally Graded Plates Available to Purchase

This article considers the free vibration of plates for which materials properties vary continuously though the thickness. First, an examination of results available in the literature led to the discovery that the natural frequencies of such functionally graded plates are proportional to those of isotropic plates. In the usual formulation of existing plate theories, the midplane is taken as the reference surface and the variation in material properties through the thickness leads to coupling between inplane and bending deformations. The second part of this paper shows that it is possible to select a different reference plane so that this coupling is eliminated and the motion of the graded plate is governed by the same equation as that of homogeneous isotropic plates. This explains the relationship between the natural frequencies that was observed in the results presented by previous investigators. The study of functionally graded plate is made much simpler and results available for isotropic plates can be used directly.