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Three-Dimensional Vibrations of a Ring on an Elastic Foundation

Published online by Cambridge University Press:  04 July 2016

S. S. Rao
S. S. Rao*
Affiliation:
Division of Solid Mechanics, Structures and Mechanical Design, Case Western Reserve University, Cleveland, USA
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Extract

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.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 75 , Issue 726 , June 1971 , pp. 417 - 419
Copyright
Copyright © Royal Aeronautical Society 1971 

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Footnotes

*

On leave from Indian Institute of Technology, Kanpur, India.

References

1. Rao, S. S. and Sundararajan, V. Inplane Flexural Vibrations of Circular Rings, Journal of Applied Mechanics, Transactions of the ASME, series E, Vol. 36, September 1969.Google Scholar
2. Love, A. E. H. A Treatise on the Mathematical Theory of Elasticity, Fourth Edition, Dover Publications, New York, 1944.Google Scholar
3. Vlasov, V. Z. and Leontév, U. N. Beams, Plates and Shells on Elastic Foundations (translation from Russian), Israel Program for Scientific Translations, Jerusalem, 1966. Also NASA TTF-337.Google Scholar
4. Rodriguez, D. A. Three-dimensional Bending of a Ring on an Elastic Foundation, Journal of Applied Mechanics, Transactions of the ASME, series E, Vol. 28, September 1961.Google Scholar