The Quasi-Static Approximation of Heat Waves in Anisotropic Thermo-Elastic Media
Shaohua Guo
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DOI: 10.4236/am.2010.15054   PDF    HTML     6,276 Downloads   10,417 Views  

Abstract

The equilibrium equations of anisotropic media, coupled to the heat conduction equations, are studied here based on the standard spaces of the physical presentation, in which an new thermo-elastic model based on the second law of thermodynamics is induced. The uncoupled heat wave equation for anisotropic media is deduced. The results show that the equation of heat wave is of the properties of dissipative waves. In final part of this paper, we discuss the propagation behaviour of heat waves for transversely isotropic media.

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S. Guo, "The Quasi-Static Approximation of Heat Waves in Anisotropic Thermo-Elastic Media," Applied Mathematics, Vol. 1 No. 5, 2010, pp. 411-415. doi: 10.4236/am.2010.15054.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] H. Lord and Y. Shulman, “A Generalized Dynamical Theory of Thermo-Elasticity,” Journal of the Mechanics and Physics, Vol. 15, No. 5, 1967, pp. 299-309.
[2] R, Dhaliwal and H. Sherief, “Generalized Thermoe-lasticity for Anisotropic Media,” The Quarterly of Applied Mathematics, Vol. 33, Vol. 1, 1980, pp. 1-8.
[3] A. E. Green and K. E. Lindsay, “Thermoelasticity,” Journal of Elasticity, Vol. 2, 1972, pp. 1-7.
[4] X. G. Tian, Y. P. Shen, et al., “A Direct Finite Element Method Study of Generalized Thermoelastic Problems,” International Journal of Solids and Structures, Vol. 43, No. 7-8, 2006, pp. 2050-2063.
[5] T. C. Chen and C. I. Weng, “Generalized Coupled Transient Thermoelastic Plane Problems by Laplace Transform/Finite Element Method,” Journal of Applied Mechanics, Vol. 55, No. 2, 1988, pp. 377-382.
[6] J. H. Prevost and D. Tao, “Finite Element Analysis of Dynamic Coupled Thermoelasticity Problems with Rela- xation Times,” Journal of the Mechanics and Physics, Vol. 50, 1983, pp. 817-822.
[7] S. H. Guo, “An Eigen Theory of Rheology for Complex Media,” Acta Mechanica, Vol. 182, 2007, pp. 985-992.
[8] S. H. Guo, “An Eigen Theory of Electromagnetic Waves Based on the Standard Spaces,” International Journal of Engineering Science, Vol. 47, 2009, pp. 405-412.
[9] S. H. Guo, “An Eigen Theory of Waves in Piezoelectric Solids,” Acta Mechanica Sinica, Vol. 26, No. 2, 2010, pp. 241-246.
[10] S. H. Guo, “An Eigen Theory of Electro-Magnetic Acoustic Waves in Magnetoelectroelastic Media,” Acta Mechanica, Vol. 211, No. 1-2, 2010, pp. 173-180.

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