Effects of Elastic Foundation on the Vibration of Laminated Non-Homogeneous Orthotropic Circular Cylindrical Shells

Abstract

In this paper an analytical procedure is given to study the free vibration characteristics of laminated non-homogeneous orthotropic thin circular cylindrical shells resting on elastic foundation, accounting for Karman type geometric non-linearity. At first, the basic relations and modified Donnell type stability equations, considering finite deformations, have been obtained for laminated thin orthotropic circular cylindrical shells, the Young's moduli of which varies piecewise continuously in the thickness direction. Applying Galerkin method to the latter equations, a non-linear time dependent differential equation is obtained for the displacement amplitude. The frequency is obtained from this equation as a function of the shell displacement amplitude. Finally, the effect of elastic foundation, non-linearity, non-homogeneity, the number and ordering of layers on the frequency is found for different mode numbers. These results are given in the form of tables and figures. The present analysis is validated by comparing results with those in the literature.