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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

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