A Semianalytical Approach for Free Vibration Characteristics of Functionally Graded Spherical Shell Based on First-Order Shear Deformation Theory

This paper describes a unified solution to investigate free vibration solutions of functionally graded (FG) spherical shell with general boundary restraints. The analytical model is established based on the first-order shear deformation theory, and the material varies uniformly along the thickness of FG spherical shell which is divided into several sections along the meridian direction. The displacement functions along circumferential and axial direction are, respectively, composed by Fourier series and Jacobi polynomial regardless of boundary restraints. The boundary restraints of FG spherical shell can be easily simulated according to penalty method of spring stiffness technique, and the vibration solutions are obtained by Rayleigh-Ritz method. To verify the reliability and accuracy of the present solutions, the convergence and numerical verification have been conducted about different boundary parameters, Jacobi parameter, etc. The results obtained by the present method closely agree with those obtained from the published literatures, experiments, and finite element method (FEM). The impacts of geometric dimensions and boundary conditions on the vibration characteristics of FG spherical shell structure are also presented.