Vibration analysis of FGM cylindrical shells under various boundary conditions

Abstract

In this paper, a unified analytical approach is proposed to investigate vibrational behavior of functionally graded shells. Theoretical formulation is established based on Sanders’ thin shell theory. The modal forms are assumed to have the axial dependency in the form of Fourier series whose derivatives are legitimized using Stokes transformation. Material properties are assumed to be graded in the thickness direction according to different volume fraction functions such as power-law, sigmoid, double-layered and exponential distributions. A FGM cylinderical shell made up of a mixture of ceramic and metal is considered. The Influence of some commonly used boundary conditions, the effect of changes in shell geometrical parameters and variations of volume fraction functions on the vibration characteristics are studied by comparing the results from the present theory with those from the First order Shear Deformation Theory (FSDT). Furthermore, the results obtained for a number of particular cases show good agreement with those available in the open literature. The simplicity and the capability of the present method are also discussed.