Natural frequencies and mode shapes of an orthotropic thin shell of revolution

A method is developed to determine the free vibration characteristics of an orthotropic thin shell of revolution of arbitrary meridian. A solution is given within the context of the Sanders–Budiansky shell theory and using the differential quadrature method (DQM). Numerical examples for frequencies and mode shapes are given for a complete toroidal shell. Both completely free shells, and shells with circumferential line supports are considered. Close agreement is observed in comparisons with previously published results and with results obtained using the finite element method. The paper ends with a set of appropriate conclusions.