Variable kinematic models applied to free-vibration analysis of functionally graded material shells

Closed-form solutions of free-vibration problems of simply supported multilayered shells made of Functionally Graded Material have been examined in the present paper. A variable kinematic shell model, which is based on Carrera's Unified Formulation is extended, in this work, to dynamic shell cases. Classical shell theories are compared to refined ones as well as to layer-wise kinematics and mixed assumptions based on the Reissner mixed variational theorem. A comparison with the few results available in the open literature is presented and conclusions are drawn regarding the accuracy of classical and advanced shell modeling to evaluate lower and higher vibration modes as well as the behavior of these modes in the shell thickness direction.