Free Transverse Vibrations of Non-Homogeneous Circular Plates of Linearly Varying Thickness

Abstract

This paper analyses free transverse axisymmetric vibrations of non-homogeneous circular plates of linearly varying thickness on the basis of classical plate theory. The non-homogeneity of plate material is assumed to arise due to variation in Young’s Modulus and density along radial direction. An approximate solution has been obtained using Ritz method. The basis functions have been chosen to satisfy the essential boundary conditions. Convergence to four digit exactitude is demonstrated for first three natural frequencies of plates. Numerical results are presented for circular plates with clamped, simply supported and free boundary conditions. This study investigates the effect of various parameters namely non-homogeneity parameter, density parameter and taper parameter on the natural frequencies of circular plates for first three modes of vibration. Results in some special cases are compared with existing solutions available from analytical and other numerical methods, which show an excellent agreement.