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Oscillations of a rigid sphere embedded in an infinite elastic solid

I. Torsional oscillations

Published online by Cambridge University Press:  24 October 2008

P. Chadwick  and
E. A. Trowbridge
P. Chadwick
Affiliation:
School of Mathematics and Physics, University of East Anglia
E. A. Trowbridge
Affiliation:
Department of Mathematics, Lanchester College of Technology, Coventry
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Abstract

A detailed study is made of angular oscillations of small amplitude about a fixed axis of a rigid sphere embedded in an infinite elastic solid. Three modes of vibration of the sphere are considered: steady oscillations arising from the application of a periodic torque; forced oscillations produced by an arbitrary time-dependent torque; and free oscillations excited by an impulsive torque. Due to the transfer of energy to the surrounding material by the radiation of an elastic shear wave, free oscillations of the sphere are damped, the principal parameter affecting the damping being the density contrast between the sphere and its surroundings. Illustrative numerical results, referring to steady and free oscillations of the sphere, are presented in graphical form.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 1189 - 1205
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Chadwick, P. and Trowbridge, E. A.Proc. Cambridge Philos. Soc. 63 (1967), 1207–1227.CrossRefGoogle Scholar
(2)Lord, Rayleigh, The theory of sound, vol. II (Dover, New York, 1945).Google Scholar
(3)Lamb, H.Proc. London Math. Soc. Ser. 1, 32 (1900), 120–150.CrossRefGoogle Scholar
(4)Lamb, H.Proc. London Math. Soc. Ser. 1, 32 (1900), 208–211.CrossRefGoogle Scholar
(5)Love, A. E. H.Proc. London Math. Soc. Ser. 2, 2 (1904), 88–113.Google Scholar
(6)Chadwick, P. and Trowbridge, E. A.Proc. Cambridge Philos. Soc. 63 (1967), 1177–1187.CrossRefGoogle Scholar
(7)Truesdell, C. and Toupin, R. A.The classical field theories. Handbuch der Physik (ed. Flügge, S.), Band III/l, pp. 226–793. (Springer-Verlag, Berlin, 1960).Google Scholar
(8)Chadwick, P. and Powdrill, B.Int. J. Engng Sci. 3 (1965), 561–595.CrossRefGoogle Scholar
(9)Kanwal, R. P.J. Math. Phys. 44 (1965), 275–283.CrossRefGoogle Scholar
(10)Williams, W. E.Quart. J. Mech. Appl. Math. 19 (1966), 413–416.CrossRefGoogle Scholar
(11)Kanwal, R. P.J. Fluid Mech. 19 (1964), 631–636.CrossRefGoogle Scholar
(12)Williams, W. E.J. Fluid Mech. 25 (1966), 589–590.CrossRefGoogle Scholar
(13)Hill, J. L.J. Acoust. Soc. Amer. 40 (1966), 376–379.CrossRefGoogle Scholar
(14)Lamb, H.Hydrodynamics, 6th edn. (Cambridge University Press, 1932).Google Scholar
(15)Jeffreys, H.Monthly Not. Roy. Astr. Soc. Geophys. Suppl. 2 (1931), 407–416.CrossRefGoogle Scholar
(16) Das Gupta, S. C.Geofis. Pura Appl. 27 (1954), 1–6.CrossRefGoogle Scholar
(17)Chakraborty, S. K.Geofis. Pura Appl. 33 (1956), 17–22.CrossRefGoogle Scholar
(18)Kupradze, V. D.Progress in solid mechanics (ed. Sneddon, I. N. and Hill, R.), vol. III (North-Holland, Amsterdam, 1963).Google Scholar
(19)Friedlander, F. G.Sound pulses (Cambridge University Press, 1958).Google Scholar
(20)Chadwick, P.Amer. Math. Monthly 69 (1962), 291–292.CrossRefGoogle Scholar
(21)Trowbridge, E. A. Thesis, University of Sheffield, 1964.Google Scholar