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On the Green function of the Lord–Shulman thermoelasticity equations.
- Source :
-
Geophysical Journal International . Jan2020, Vol. 220 Issue 1, p393-403. 11p. - Publication Year :
- 2020
-
Abstract
- Thermoelasticity extends the classical elastic theory by coupling the fields of particle displacement and temperature. The classical theory of thermoelasticity, based on a parabolic-type heat-conduction equation, is characteristic of an unphysical behaviour of thermoelastic waves with discontinuities and infinite velocities as a function of frequency. A better physical system of equations incorporates a relaxation term into the heat equation; the equations predict three propagation modes, namely, a fast P wave (E wave), a slow thermal P wave (T wave), and a shear wave (S wave). We formulate a second-order tensor Green's function based on the Fourier transform of the thermodynamic equations. It is the displacement–temperature solution to a point (elastic or heat) source. The snapshots, obtained with the derived second-order tensor Green's function, show that the elastic and thermal P modes are dispersive and lossy, which is confirmed by a plane-wave analysis. These modes have similar characteristics of the fast and slow P waves of poroelasticity. Particularly, the thermal mode is diffusive at low thermal conductivities and becomes wave-like for high thermal conductivities. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0956540X
- Volume :
- 220
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Geophysical Journal International
- Publication Type :
- Academic Journal
- Accession number :
- 140358050
- Full Text :
- https://doi.org/10.1093/gji/ggz453