Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Kovalev V. A., Radaev Y. N., Semenov D. A. Coupled Dynamic Problems of Hyperbolic Thermoelasticity. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2009, vol. 9, iss. 4, pp. 94-127. DOI: 10.18500/1816-9791-2009-9-4-2-94-127

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
Full text:
(downloads: 149)

Coupled Dynamic Problems of Hyperbolic Thermoelasticity

Kovalev Vladimir Aleksandrovich, Moscow City Government University of Management Moscow, Russia
Radaev Yuri Nickolaevich, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
Semenov D. A., Samara National Research University

In the present paper in the framework of the linear non-dissipative coupled thermoelasticity (GNII, hyperbolic thermoelasticity), treating the heat transport as propagation with finite speed of undamped waves of second sound, harmonic coupled thermoelastic waves propagating in an infinite free from tractions thermoisolated cylinder are studied. Dispersionrelation is derived for this type of thermoelastic waves for an arbitrary azimuthal order. Numerical results for wave numbers depending on frequency are obtained. Special attention is paid to the waves of the second azimuthal order. The study follows investigation of weak discontinuities propagation in GNII media by the Thomas – Hadamard technique and analysis of plane harmonic thermoelastic coupled waves. 

  1. Новацкий В. Вопросы термоупругости. М.: Изд-во АН СССР, 1962. 364 c.
  2. Новацкий В. Динамические задачи термоупругости. М.: Мир, 1970. 256 c.
  3. Joseph D.D. Heat waves // Rev. Modern Physics. 1989. V. 61, № 1. P. 41–73.
  4. Green A.E., Naghdi P.M. On undamped heat waves in an elastic solid // J. Therm. Stress. 1992. V. 15. P. 253– 264.
  5. Green A.E., Naghdi P.M. Thermoelasticity without energy dissipation // J. Elasticity. 1993. V. 31. P. 189– 208.
  6. Bargmann S., Steinmann P. Theoretical and computational aspects of non-classical thermoelasticity // Comput. Methods Appl. Mech. Engrg. 2006. V. 196. P. 516–527.
  7. Kalpakides V.K., Maugin G.A. Canonical formulation and conservation laws of thermoelasticity without dissipation // Reports in Mathematical Physics. 2004. V. 53. P. 371–391.
  8. Puri P., Jordan P.M. On the propagation of plane waves in type-III thermoelastic media // Proc. R. Soc. Lond. A. 2004. V. 460. P. 3203–3221.
  9. Pochhammer L. Uber Fortpflanzungsgeschwindigkeiten kleiner Schwingungen in einem unbegrenzten isotropen Kreiszylinder // J. reine angew. Math. 1876. V. 81. P. 324–336.
  10. Chree C. The equations of an isotropic elastic solid in polar and cylindrical coordinates: Their solution and application // Trans. Cambridge Philos. Soc. 1889. V. 14. P. 250–369.
  11. Снеддон И.Н., Берри Д.С. Классическая теория упругости. М.: Физматлит, 1961. 220 c.
  12. Кольский Г. Волны напряжения в твердых телах. М.: Изд-во иностр. лит., 1955. 192 c.
  13. Love A.E.H. A treatise on the mathematical theory of elasticity. N.Y.: Dover Publications, 1944. 644 p.
  14. Bancroft D. The velocity of longitudinal waves in cylindrical bars // Phys. Rev. 1941. V. 59. P. 588–593.
  15. Hudson G.E. Dispersion of elastic waves in solid circular cylinders // Phys. Rev. 1943. V. 63. P. 46–51.
  16. Miklowitz J. The theory of elastic waves and waveguides. Amsterdam; N.Y.; Oxford.: North-Holland Publishing Company, 1978. 618 p.
  17. Graff K.F. Wave motion in elastic solids. N.Y.: Dover Publications, 1991. 649 p.