Prediction of dynamic behaviour of FGM shells under arbitrary boundary conditions

In this study, a general analytical approach is presented to investigate vibrational behavior of functionally graded shells. Theoretical formulations, based on first order shear deformation shell theory, take into consideration transverse shear deformation and rotary inertia effects. The modal forms are assumed to have the axial dependency in the form of Fourier series whose derivatives are legitimized using Stoke’s transformation. Material properties are assumed to be temperature-dependent and graded in the thickness direction according to different volume fraction functions. These functions are assumed to have power–law, sigmoid and exponential distributions. A FGM cylindrical shell made up of a mixture of ceramic and metal is considered. The Influence of some commonly used boundary conditions, the effect of variations of volume fractions and shell geometrical parameters on the vibration characteristics are studied. The results obtained for a number of particular cases show good agreement with those available in the literature.