Natural frequencies of an orthotropic thin toroidal shell of elliptical cross-section

A method is presented to determine the natural frequencies of an orthotropic thin toroidal shell of elliptical cross-section. The solution is based on the classical Sanders–Budiansky shell theory and uses the differential quadrature method (DQM) to obtain numerical results. The appropriate scheme for the selection of the sampling points in the DQM for shells of elliptical cross-section is indicated. Values for frequencies are given for complete toroidal shells, which are entirely free of supports, or with a support along a circumferential line. The results obtained from the method show close agreement with previously published results, and with results obtained using the finite element method.