Vibration Study of three layered cylindrical shells with variable materials of functionally graded layers with and without ring supports

Abstract

In this work, we study vibrations of three-layered circular cylinder-shaped shells with and without one ring support along the shell length. The implementation of Rayleigh-Ritz method has been done under the Sanders’ shell theory to obtain the shell frequency equations. Natural frequencies (NFs) have been attained for the present model problem under six end point conditions. Use of characteristic beam functions has been made for the estimation of the dependence of axial modals. The impact of layer material variations with ring support has been considered for many ring positions. Also the effect of volume fraction laws has been investigated. This analysis has been performed for various physical parameters. The MATLAB software has been used to solve the problem. Numerous comparisons of values of shell frequencies have been done with available models of such types of results to verify accuracy of the present formulation and demonstrate its numerical efficiency.