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On the forced torsional oscillations of an elastic cylinder

Published online by Cambridge University Press:  24 October 2008

R. Shail
R. Shail
Affiliation:
Department of Applied Mathematics, The University of Liverpool
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Abstract

The forced torsional motion of a semi-infinite isotropic right-circular elastic cylinder is studied in this paper, the vibrations being excited by a harmonically oscillating rigid disc, securely attached to the plane face of the cylinder. Two distinctsituations are considered, namely, when the curved surface of the cylinder is clamped and when it is stress free. In both cases the problem is reduced to the solution of a Fredholm integral equation of the second kind which can be solved iteratively when the frequency of oscillation is small and the cylinder radius large. Using the iterative solutions, approximate expressions are deduced for the distribution of shear stress under the disc and the driving couple required. In an appendix a discussion is given of a mathematically similar problem in the theory of the swirling flow of a perfect fluid.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 4 , October 1965 , pp. 955 - 967
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

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