Free vibration analysis of Lévy-type functionally graded spherical shell panel using a new exact closed-form solution

An exact closed-form analysis for describing the natural vibrations of a FG moderately thick spherical shell panel is developed. The strain–displacement relations of Donnell and Sanders theories are used to obtain the exact solutions. The shell has two opposite edges simply supported (i.e., Lévy-type). The material properties change continuously through the thickness of the shell, which can vary according to a power-law distribution of the volume fraction of the constituents. The new auxiliary and potential functions are employed to exactly decouple the governing equations of the vibrated spherical shell panel, leading to the exact closed-form frequency equation in the form of determinant. The accuracy and validity of the solutions are established with the aid of a 3D finite element analysis as well as by comparing the results with the data reported in the literature. The effects of various stretching–bending couplings on the frequency parameters are discussed.