Abstract
The problem of vibrations of a circular ring on an elastic foundation finds application in the study of vibrations of gears mounted on elastic shafts and launching vehicles having a ring-stiffened shell structure.The inplane flexural vibrations of a circular ring were investigated by many authors in connection with the study of vibrations of gears and frames of electrical machines. The transverse vibrations of a thin ring of circular cross-section were first investigated in 1890 by Michell. There appears to be less amount of work in the literature which deals with the effects of rotatory inertia and shearing deformation on the transverse vibrations of rings. In the present investigation, flexural vibrations of a circular ring on an elastic foundation involving both displacements at right angles to the plane of the ring and twist are studied. The foundation is considered to provide restraints against the transverse and torsional motions of the cross-section of the ring linearly.
Published Version
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