Abstract
The coupled twist-bending vibrations of complete, incomplete and transversely supported rings are investigated. The governing equations of motion are developed from Hamilton's principle by considering the effects of rotatory inertia and shearing deformation. The results are compared with those given by the classical theory which neglects the effects of shear and rotatory inertia. The frequencies of vibration of a ring with rectangular cross-section are compared with the available experimental values and it is found that the theoretical prediction would be closest to the true frequencies if the effect of shear deformation is also considered. Natural frequencies of a ring supported transversely at two, three and four points are found. The vibration characteristics of incomplete rings are studied by varying the boundary conditions, the ring's subtended angle and the stiffness parameter EI/C.
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