Free vibrations of toroidal shells

In this paper, the free vibrations of toroidal shells with circular cross section are analyzed by using a thin 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 in a discussion of numerical results. The frequencies obtained by this analytical method are compared with those by other approximate methods and the validities of the present exact solution are confirmed. (author)