Vibration of functionally graded cylindrical shells with ring support

In this paper, the vibrational behavior of functionally graded cylindrical shells with intermediate ring supports is studied. Theoretical formulation is established based on Sanders’ thin shell theory. The governing equations of motion are derived, using an energy functional and by applying the Ritz method. Using an appropriate set of displacement functions, the energy equations lead to an eigenvalue problem whose roots are the natural frequencies of vibration. Material properties are assumed to be graded in the thickness direction, according to the power-law volume fraction function. A functionally graded cylindrical shell, made up of a mixture of ceramic and metal, is considered. The influence of some commonly used boundary conditions and the effect of changes in shell geometrical parameters and variations in ring support position on vibration characteristics are studied. The results obtained for a number of particular cases show good agreement with those available in the open literature.