Axisymmetric Free Vibration of Shallow Spherical Shells With a Circular Rigid Insert

Abstract

A general solution for the third-order partial differential equations for the axisymmetric free vibration of thin isotropic shallow spherical shells with a rigid insert 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. Both linear and non-linear boundary conditions are applied and the results are compared. The relationship between the vibrational frequency, mode shape and the size of the rigid insert is discussed.