Free vibrations of elastic circular toroidal shells

In this paper, the free vibrations of elastic in vacuo circular toroidal shells under different boundary conditions are studied using the linear Sanders thin shell theory. Beam functions are used to describe the motion along the meridional direction whilst trigonometric functions are used to represent the deformation of the cross section. It is shown that both the natural frequencies and the mode shapes can be accurately predicted as long as the employed beam functions satisfy the boundary conditions at the ends of the shells. The dependence of the free vibration characteristics of an elastic toroidal shell upon boundary conditions and toroidal to cross-sectional radius ratio is also illustrated and explained in this paper.