Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-26T14:22:21.903Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1) Bycroft, G. N. Philos. Trans. Roy. Soc. London Ser. A, 248 (1955–1956), 327–368.Google Scholar
(2) Collins, W. D. Quart. J. Mech. Appl. Math., 14 (1961), 101–117.CrossRefGoogle Scholar
(3) Collins, W. D. Proc. London Math. Soc., (3) 12 (1962), 226–244.CrossRefGoogle Scholar
(4) Collins, W. D. Proc. London Math. Soc., (3) 15 (1965), 167–192.CrossRefGoogle Scholar
(5) Fraenkel, L. E. Proc. Roy. Soc. Ser. A, 233 (1965), 506–526.Google Scholar
(6) Jones, D. S. Comm. Pure Appl. Math., 9 (1956), 713–746.CrossRefGoogle Scholar
(7) Love, A. E. H. Mathematical theory of elasticity, (Cambridge, 1952).Google Scholar
(8) Mccoy, J. J. Z. Angew. Math. Phys., 15 (1964), 456–465.CrossRefGoogle Scholar
(9) Reissner, E. and Sagoci, H. F. J. Appl. Phys., 15 (1944), 652–654.CrossRefGoogle Scholar
(10) Sagoci, H. F. J. Appl. Phys., 15 (1944), 655–662.CrossRefGoogle Scholar
(11) Sneddon, I. N. and Srivastav, R. P. Proc. Roy. Soc. Edinburgh Sect. A, 66 (1964), 150–160.Google Scholar
(12) Srivastav, R. P. Proc. Roy. Soc. Edinburgh Sect. A, 66 (1964), 161–172.Google Scholar
(13) Trustrum, K. J. Fluid Mech., 18 (1964), 415–432.CrossRefGoogle Scholar
(14) Watson, G. N. Theory of Bessel Functions, (Cambridge, 1958).Google Scholar
(15) Wei, Lai. J. Fluid Mech., 18 (1964), 587–594.Google Scholar
(16) Williams, W. E. Proc. Roy. Soc. Ser. A, 267 (1962), 77–87.Google Scholar
(17) Williams, W. E. Z. Angew. Math. Phys., 13 (1962), 133–152.CrossRefGoogle Scholar
(18) Williams, W. E. J. London Math. Soc., 38 (1963), 119–122.CrossRefGoogle Scholar