Abstract
In this investigation, the free vibrations of fluid-filled toroidal shells are studied. An inviscid, irrotational and incompressible liquid is considered. Laplace's equation for the fluid is solved by using the associated Legendre functions. The toroidal shell's equations are established on the basis of Love's general thin shell theory. The equations of free vibration of the coupled system is obtained and solved by using certain trigonometric series expansions. A comparison of the calculated frequencies and corresponding mode shapes of a dry toroidal shell shows good agreement with available results. Calculations are presented for several examples of fluid-filled toroidal shells. The effects of various parameters upon natural frequencies are illustrated.
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