On axisymmetric vibration of shallow spherical shells with fixed circular cutout

Abstract A general solution of the third-order partial differential equations of a thin isotropic shallow spherical shell with a fixed circular cutout subject to axisymmetric free vibration is presented in this paper. The frequency equation in terms of Bessel functions as well as modified Bessel functions is solved for the fundamental vibrational frequency and mode shape. Solutions for different size cutouts are obtained and compared to a corresponding finite element model. The relationship between the vibrational frequency and mode shape and the size of the fixed cutout is discussed.