A unified accurate solution for vibration analysis of arbitrary functionally graded spherical shell segments with general end restraints

A unified accurate solution procedure for free vibration analysis of arbitrary functionally graded spherical shell segments with general end restraints is presented. The material properties of the spherical shells are assumed to change continuously in the thickness direction and two different four-parameter power-law distributions are considered. The proposed method is formulated by the Ritz procedure on the basis of the first-order shear deformation shell theory. Each of admissible functions, regardless of boundary conditions, is composed of a standard Fourier cosine series and several auxiliary functions introduced to ensure and accelerate the convergence of series representations. The accuracy and reliability of the current solution are validated by comparing the results with existing results and those generated from the finite element analyses, and numerous new results for functionally graded spherical shells subjected to elastic restraints are presented, which can serve as the benchmark solutions for other computational techniques in the future research. The effects of the boundary conditions, power-law exponents, and shell segments on the free vibrations of the spherical shells are also investigated, and some interesting insights into the parameter effects on frequency behaviors are illustrated.