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The Quarterly Journal of Mechanics and Applied Mathematics 2000 53(1):1-25; doi:10.1093/qjmam/53.1.1
© 2000 by Oxford University Press
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Wave stability for incompressibility at uniform temperature or entropy in generalized isotropic thermoelasticity

DJ Leslie and NH Scott

( School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK )

This work is an extension of Leslie and Scott (Q. Jl Mech. appl. Math. 51 (1998) 191-211) to the theory of generalized isotropic thermoelasticity in which Fourier's constitutive equation for heat conduction is replaced by one in which a relaxation time {tau}0 is associated with the heat-flux vector. The effect is to give finite speeds of wave propagation at all frequencies. For an unconstrained isotropic material in generalized thermoelasticity two longitudinal waves may propagate in each direction. We show that if these two modes intersect in the complex plane of squared wave speeds as frequency varies then they intersect in two semicircles in the lower half of this complex plane (which guarantees stability). The stability/instability properties of waves propagating in a thermomechanically constrained material are found to be unchanged by the existence of {tau}0 > 0. In particular, of the two longitudinal waves which may propagate in each direction through a generalized isotropic thermoelastic material which is incompressible at uniform temperature, one is stable and the other unstable. If instead the isotropic material is incompressible at uniform entropy it is found that the single longitudinal wave which now propagates has a mode which occupies a semicircle in the lower half of the complex plane introduced above (and so is stable). This semicircle shrinks as {tau}0 increases.


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This article has been cited by other articles:


Home page
 Mathematics and Mechanics of SolidsHome page
D. J. Leslie and N. H. Scott
Wave Stability for Constrained Materials in Anisotropic Generalized Thermoelasticity
Mathematics and Mechanics of Solids, October 1, 2004; 9(5): 513 - 542.
[Abstract] [PDF]

Home page
 Mathematics and Mechanics of SolidsHome page
D. J. Leslie and N. H. Scott
Wave Stability for Near-Incompressibility at Uniform Temperature or Entropy in Generalized Isotropic Thermoelasticity
Mathematics and Mechanics of Solids, June 1, 2000; 5(2): 157 - 202.
[Abstract] [PDF]


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