A new shear deformation shell theory for free vibration analysis of FG sandwich shells

In recent years, many researches have been published dealing with the mechanical responses of shells with variable cross-sectional mechanical properties such as sandwich, functionally graded and laminated composites shells. In the present paper, a simple and efficient shear deformation theory is formulated for the free vibration response of functionally graded sandwich shells. The main advantage of this theory is its reduced number of unknowns and their related governing equations and theses tend to be highly compared to others shear deformation shell theories. Two kinds of FG sandwich shells are studied with respect to their geometrical configuration and material properties. The first kind is composed of FG facesheet and homogeneous core and the other is formed by homogeneous facesheet and FG core. The governing equations of motion for the free vibration analysis are obtained using Hamilton's principle. The closed form solutions are sought by using the Navier's method for eigenvalue problems. The accuracy and efficiency of the present theory are established and proved by comparing obtained numerical results with those predicted by other higher order shear deformation shell theories. The influences of various parameters such as material distribution, thickness of the core and the facesheet of sandwich shell and curvature ratios are studied, discussed and reported as significant rate sensitivity to predict the fundamental frequencies of FG sandwich shells.