Abstract
In this work, the vibrational frequency of two layered FGM cylindrical shell with and without the effects of internal pressure under ring support are discussed in detailed. The functionally graded materials of a cylindrical shell are designed for specific purpose and studied under various boundary conditions. The Love shell dynamical equations theory is utilized to find the relationship between the curvature displacement and strain displacement. Natural frequency vibrations are analyzed by using volume polynomial for bi-layered FGM shell under ring support both for with and without internal pressures.