Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-05T08:31:09.704Z Has data issue: false hasContentIssue false

Wave propagation in a transversely isotropic heat-conducting elastic material

Published online by Cambridge University Press:  26 February 2010

P. Chadwick
Affiliation:
School of Mathematics and Physics, University of East Anglia, Norwich.
L. T. C. Seet
Affiliation:
School of Mathematics and Physics, University of East Anglia, Norwich.
Get access

Summary

A transversely isotropic elastic material can transmit three body waves in each direction, a quasi-longitudinal (QL) wave, a quasi-transverse (QT) wave, and a purely transverse wave. When the material is able to conduct heat the properties of small amplitude QL and QT waves are modified and we consider here the analysis of such thermo-elastic interactions in plane harmonic disturbances. The modified QL and QT waves are both found to exhibit frequency-dependent dispersion and damping of the kind known to affect dilatational waves in isotropic heat-conducting elastic materials, and in addition we show that the particle paths in the associated motions are ellipses with their axes inclined to the wave normal. This latter effect is peculiar to body waves travelling in anisotropic heat-conducting elastic materials and seems not to have been studied in detail hitherto. Numerical results referring to the propagation of plane harmonic body waves in a single crystal of zinc are presented and discussed.

Type
Research Article
Copyright
Copyright © University College London 1970

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

1.Chadwick, P., Progress in solid mechanics (ed. Sneddon, I. N. and Hill, R.), Vol. I, 265328 (North-Holland: Amsterdam, 1960).Google Scholar
2.Chadwick, P., J. Mech. Phys. Solids, 10 (1962), 99109.CrossRefGoogle Scholar
3.Flavin, J. N. and Green, A. E., J. Mech. Phys. Solids, 9 (1961), 179190.CrossRefGoogle Scholar
4.Chadwick, P. and Seet, L. T. C., Article in Recent developments in classical elasticity and thermoelasticity (ed. Zorski, H. and Olesiak, Z.). Forthcoming.Google Scholar
5.McSkimin, H. J., J. appl. Phys., 26 (1955), 406409.CrossRefGoogle Scholar
6.Smithells, C. J. (ed.), Metals reference book, 4th edn. (Butterworths: London, 1967).Google Scholar
7.Long, T. R. and Smith, C. S., Acta. metall., 5 (1957), 200207.CrossRefGoogle Scholar
8.Waterman, P. C., J. appl. Phys., 29 (1958), 11901195.CrossRefGoogle Scholar
9.Boas, W. and Mackenzie, J. K., Progress in metal physics (ed. Chalmers, B.), Vol. 2, 90120 (Pergamon: Oxford, 1950).Google Scholar
10.Buchwald, V. T., Q. J. Mech. appl. Math., 14 (1961), 293317.CrossRefGoogle Scholar
11.Garabedian, P. R., Partial differential equations (Wiley: New York, 1964).Google Scholar
12.Koshlyakov, N. S., Smirnov, M. M. and Gliner, E. B., Differential equations of mathematical physics (North-Holland: Amsterdam, 1964).Google Scholar
13.Hayes, M., Proc. R. Soc., A, 274 (1963), 500506.Google Scholar
14.Post, E. J., Can. J. Phys., 31 (1953), 112119.CrossRefGoogle Scholar