Abstract
This paper presents an analysis of the free vibration of a toroidal shell with an interior partition consisting of a concentric circular cylindrical shell. For this purpose, the governing equation for vibration of a toroidal shell including a circular cylindrical shell is written as a coupled set of first-order differential equations by use of 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 system, and the frequency equation is derived in terms of the elements of the structure matrix. The method is applied to toroidal shells with interior partitions, and the natural frequencies and the mode shapes of vibration are calculated numerically.
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