This work investigates the free vibration and buckling of a two-layered cylindrical shell structure made of an elastic embedded functionally graded (FG) shell subjected to combined static and periodic axial forces. Such structures are widely used in chemical and nuclear reactors, space and aerial industries, and so on. Material properties of an FG cylindrical shell are considered to be temperature dependent and graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. Theoretical formulations are presented based on two different methods of the first-order shear deformation theory considering the transverse shear strains and the rotary inertias and the classical shell theory. The results obtained show that the effect of transverse shear and rotary inertias on free vibration of an FG cylindrical shell is dependent on the material composition, deformation mode, and geometry parameters of the shells. It is concluded that the application of an outer elastic layer increases elastic stability.
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