Axisymmetric vibrations of non-homogeneous polar orthotropic annular plates of variable thickness

Abstract

In this study of the free axisymmetric vibrations of non-homogeneous polar orthotropic annular plates of exponentially varying thickness, on the basis of the classical theory of plates, the Chebyshev collocation technique has been employed to solve the differential equation governing the transverse motion of such plates. The non-homogeneity of the plate material is assumed to arise due to the variation of Young's moduli and density which are assumed to vary exponentially with the radius vector. The effect of various plate parameters such as radii ratio, rigidity ratio, non-homogeneity and thickness variation, on the vibrational characteristics of the plate have been studied for three different boundary conditions. Normalized displacements are presented for a specified plate for the first three modes of vibration. A comparison of results with those available in the literature has been presented.