Dynamic Characteristics of Elastic Circular Toroidal Shells

In this paper, the free vibrations of incomplete toroidal shells with different meridional boundary conditions are studied based on the linear Flugge thin shell theory. The cross-section of toroidal shells is assumed to be a closed circle. The circumferential modes are represented by a series of trigonometric functions and the meridional modes are expressed as a combination of beam functions which satisfy the boundary conditions at the ends of the shell. 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. The dependence of the free vibration characteristics of elastic toroidal shell upon boundary conditions is also illustrated and explained by means of an example in this paper.