AXISYMMETRICAL FREE-VIBRATION OF SHALLOW SPHERICAL-SHELLS WITH A CIRCULAR RIGID INSERT

A general solution for the third-order partial differential equations for the axisymmetric free vibration of thin isotropic shallow spherica l shells with a rigid insert is presented in this paper. The frequency equation in terms of Bessel functions as well as modified Bessel func tions is solved for the fundamental vibrational frequency and mode sha pe. Both linear and non-linear boundary conditions are applied and the results are compared. The relationship between the vibrational freque ncy, mode shape and the size of the rigid insert is discussed.