Abstract
In this paper, the free vibrations of thick toroidal shells with circular cross section are analyzed by using an improved thick shell theory. The equations of motion and the boundary conditions are derived from the stationary conditions of the Lagrangian of the toroidal shell. The equations of motion are solved exactly by a power series expansion and then natural frequencies and mode shapes are obtained. Effects of various parameters upon natural frequencies are clarified through analysis of numerical results. The results by the present improved thick shell theory are compared with those by the classical thin shell theory and the effects of the rotatory inertia and the shear deformation upon natural frequencies and mode shapes are clarified.
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