Abstract
In this research, vibration frequency analysis of three layered functionally graded material (FGM) cylinder-shaped shell is studied with FGM central layer and the internal and external layers are of homogenous material. Strain and curvature-displacement relations are taken from Sander's shell theory. The shell frequency equation is obtained by employing the Rayleigh Ritz method. Influence on natural frequencies (NFs) is observed for various thickness of the middle layer. The characteristics beam functions are used to estimate the dependence of axial modal. Results are obtained for thickness to radius ratios and length to radius ratios for different edge conditions. The validity of this method is checked for numerous results in the open literature.