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Interchange of modal properties in the propagation of harmonic waves in heat-conducting materials

Published online by Cambridge University Press:  17 April 2009

P. Chadwick
P. Chadwick
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland, and School of Mathematics and Physics, University of East Anglia, Norwich, England.
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Abstract

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A study is made of the secular equation governing the propagation of plane harmonic waves of small amplitude in a continuum which is able to conduct heat. This equation defines an algebraic function, called the modal function, whose regular branches specify the slownesses of the possible modes of harmonic wave propagation as functions of the frequency. At each extreme of the frequency range one mode is diffusive in type and the others wave-like, and we suppose here that there is a single wave-like mode which produces changes of temperature. In this case the mode which is diffusive in type at low frequencies is wave-like or diffusive in the high-frequency limit according as the thermoelastic coupling constant (a dimensionless measure of the strength of thermo-mechanical interaction in the continuum) does or does not exceed unity. This property is shown to have a simple interpretation in terms of a Riemann surface of the modal function. The results obtained are quite general, referring to principal longitudinal waves in a homogeneously deformed isotropic heat-conducting elastic material, to dilatational disturbances of a stress-free configuration of such a material, and to acoustic waves in a heat-conducting inviscid fluid.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 8 , Issue 1 , February 1973 , pp. 75 - 92
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Bliss, Gilbert Ames, Algebraic functions (Colloquium Publ. 16. Amer. Math. Soc., New York, 1933).Google Scholar
[2]Chadwick, P., “Thermoelasticity. The dynamical theory”, Progress in solid mechanics, Vol. I, 265–328 (edited by Sneddon, I.N. and Hill, R., North-Holland, Amsterdam, 1960).Google Scholar
[3]Chadwick, P. and Seet, L.T.C., “Wave propagation in a transversely isotropic heat-conducting elastic material”, Mathematika 17 (1970), 255–274.CrossRefGoogle Scholar
[4]Craine, R.E. and Johnson, A.F., “Acoustic wave propagation in a binary mixture of inviscid fluids”, J. Sound Vib. 20 (1972), 191–207.CrossRefGoogle Scholar
[5]Dillon, O.W. Jr, “Thermoelasticity when the material coupling parameter equals unity”, J. Appl. Mech. 32 (1965), 378–382.CrossRefGoogle Scholar
[6]McKinney, J.E. and Oser, H.J., “Acoustic propagation and stability within an inviscid, heat-conducting fluid”, J. Res. Nat. Bur. Standards Sect. B 74 (1970), 67–84.CrossRefGoogle Scholar
[7]Thurston, R.N., “Wave propagation in fluids and normal solids”, Physical Acoustics, Vol. I, part A, 1–110 (edited by Mason, W.P.. Academic Press, New York and London, 1964).Google Scholar