Free vibrations of thin elastic spherical shells

Abstract This paper is devoted to the problem of free, harmonic vibrations of thin, elastic, spherical shells. The differential equations are rederived in an invariant form together with the appropriate kinematic and static boundary conditions. The complete solution is presented for axisymmetric and non-axisymmetric vibrational modes for a shell in the shape of a spherical zone with two boundaries. The hitherto unsolved problem of non-axisymmetric vibrations of a spherical shell with a circular opening is included as a special case. Numerical examples are given covering a variety of boundary conditions and a wide range of the geometrical parameters.