Free Vibration of a Joined Spherical Shell-Annular Plate System

Abstract

An analysis is presented for the free vibration of a joined spherical shell-annular plate system. For this purpose, the governing equation of vibration of a spherical shell including an annular plate as a special case are written as a coupled set of first order differential equations using the transfer matrix of the shell. Once the transfer matrix has been determined by quadrature of the equations, the entire structure matrix is obtained by the product of the transfer matrices and the point matrix at the joint of the shell-plate system, and the frequency equation is derived in terms of the elements of the structure matrix. The method is applied to the system clamped at the outer edge of the plate, and the natural frequencies and the mode shapes of vibration are calculated numerically.