Skip to main content

Propagation of harmonic perturbations in a thermoelastic medium with heat relaxation


The propagation of plane harmonic waves in a thermoelastic medium with heat-flux relaxation is studied; in particular, the dependences of the temperature and displacement on the coordinate are analyzed in a coupled formulation. The dependences of the group and phase velocities on frequency are investigated. The influence of the frequency and parameters of the material on the amplitude of thermoelastic waves is examined. The results are compared with the available results obtained using classical thermoelasticity theory.

This is a preview of subscription content, access via your institution.


  1. A. G. Shashkov, V. A. Bubnov, and S. Yu. Yanovskii, Wave Phenomena of Heat Conduction: Systematic and Structural Approach (Nauka Tekhnika, Minsk, 1993) [in Russian].

    Google Scholar 

  2. T. Q. Qiu and C. L. Tien, “Short-Pulse Laser Heating on Metals,” Int. J. Heat Mass Transfer, No. 35, 719–726 (1992).

    Google Scholar 

  3. D. Y. Tzou, “On the Thermal Shock Wave Induced by a Moving Heat Source,” Int. J. Heat Mass Transfer., No. 111, 232–238 (1989).

    Google Scholar 

  4. S. L. Sobolev, “Transport Processes and Traveling Waves in Locally Equilibrium Systems,” Usp. Fiz. Nauk 161(3), 5–29 (1991).

    MathSciNet  Google Scholar 

  5. D. J. Jou, J. Casas Vazquez, and G. Lebon, Extended Irreversible Thermodynamics (Springer, 2010).

    MATH  Book  Google Scholar 

  6. C. C. Wang, “The Principle of Fading Memory,” Arch. Ration. Mech. Anal. 18, 343–366 (1964).

    Article  Google Scholar 

  7. D. Y. Tzou, Macro-to-Microscale Heat Transfer. The Lagging Behavior (Taylor and Francis, New York, 1997).

    Google Scholar 

  8. H. Lord and Y. Shulman, “A Generalized Dynamical Theory of Thermoelasticity,” J. Mech. Phys. Solids 15, 299–309 (1967).

    ADS  MATH  Article  Google Scholar 

  9. V. Nowacki, Dynamic Problems of Thermoelasticity (Noordhoff, Netherlands, 1975).

    Google Scholar 

  10. M. B. Babenkov, “Analysis of Dispersion Relations of a Coupled Thermoelasticity Problem with Regard to Heat-flux Relaxation,” Prikl. Mekh. Tech. Fiz. 52(6), 112–121 (2011) [Appl. Mech. Tech. Phys. 52 (6), 941–949 (2011)].

    Google Scholar 

  11. Physical Encyclopedia, Ed. by A. M. Prokhorov (Sov. Entsiklopediya, Moscow, 1988), Vol. 5, p. 80 [in Russsian].

    Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to M. B. Babenkov.

Additional information

Original Russian Text © M.B. Babenkov.


Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 54, No. 2, pp. 126–137, March–April, 2013.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Babenkov, M.B. Propagation of harmonic perturbations in a thermoelastic medium with heat relaxation. J Appl Mech Tech Phy 54, 277–286 (2013).

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI:


  • hyperbolic thermoelasticity theory
  • Maxwell-Cattaneo law
  • heat-flux relaxation
  • wave transport of heat
  • second sound