Free Vibration Characteristics of Thin Spherical Shells

Abstract

Free vibration characteristics of thin spherical shells having freely boundary conditions are analyzed. In this study, the fundamental properties of natural vibration for the spherical shells are investigated. The power function is employed as the admissible function, displacement functions satisfying the geometric boundary conditions are expressed in the form of single series. The eigenvalue problem for free vibration of the shells derived by using the Lagrange’s equation of motion, is processed numerically to acquire the natural frequencies and mode shapes. The reliability and accuracy of the present results are verified by convergence tendencies of the present solutions and comparisons of the data between the current analysis, FEM (finite element method) and published literatures. In numerical results, the variations of natural vibration characteristics of the shells due to the circumferential wavenumber and various shell geometries are illustrated.