Table of Contents
Journal of Thermodynamics
Volume 2013, Article ID 754798, 12 pages
http://dx.doi.org/10.1155/2013/754798
Research Article

Two Temperature Magneto-Thermoelasticity with Initial Stress: State Space Formulation

Department of Mathematics, G. J. University of Science and Technology, Hisar, Haryana 125001, India

Received 12 May 2013; Accepted 20 August 2013

Academic Editor: Felix Sharipov

Copyright © 2013 Sunita Deswal and Kapil Kumar Kalkal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. A. Biot, “Thermoelasticity and irreversible thermodynamics,” Journal of Applied Physics, vol. 27, no. 3, pp. 240–253, 1956. View at Publisher · View at Google Scholar · View at Scopus
  2. H. W. Lord and Y. Shulman, “A generalized dynamical theory of thermoelasticity,” Journal of the Mechanics and Physics of Solids, vol. 15, no. 5, pp. 299–309, 1967. View at Google Scholar · View at Scopus
  3. A. E. Green and K. A. Lindsay, “Thermoelasticity,” Journal of Elasticity, vol. 2, no. 1, pp. 1–7, 1972. View at Publisher · View at Google Scholar · View at Scopus
  4. D. S. Chandrasekharaiah, “Thermoelasticity with second sound: a review,” Applied Mechanics Reviews, vol. 39, pp. 355–376, 1986. View at Google Scholar
  5. D. S. Chandrasekharaiah, “Hyperbolic thermoelasticity: a review of recent literature,” Applied Mechanics Reviews, vol. 51, pp. 705–729, 1998. View at Google Scholar
  6. G. Paria, “On magneto-thermoelastic plane waves,” Proceedings of the Cambridge Philosophical Society, vol. 58, pp. 527–531, 1962. View at Google Scholar
  7. A. H. Nayfeh and S. Nemat-Nasser, “Electromagneto-thermoelastic plane waves in solids with thermal relaxation,” Journal of Applied Mechanics, vol. 39, no. 1, pp. 108–113, 1972. View at Google Scholar · View at Scopus
  8. S. K. R. Choudhuri, “Electro-magneto-thermo-elastic plane waves in rotating media with thermal relaxation,” International Journal of Engineering Science, vol. 22, no. 5, pp. 519–530, 1984. View at Google Scholar · View at Scopus
  9. M. A. Ezzat, “Generation of generalized magnetothermoelastic waves by thermal shock in a perfectly conducting half-space,” Journal of Thermal Stresses, vol. 20, no. 6, pp. 617–633, 1997. View at Google Scholar · View at Scopus
  10. M. A. Ezzat, M. I. Othman, and A. A. Smaan, “State space approach to two-dimensional electromagneto-thermoelastic problem with two relaxation times,” International Journal of Engineering Science, vol. 39, no. 12, pp. 1383–1404, 2001. View at Publisher · View at Google Scholar · View at Scopus
  11. L. Y. Bahar and R. B. Hetnarski, “State space approach to thermoelasticity,” Journal of Thermal Stresses, vol. 2, no. 1, pp. 135–145, 1978. View at Google Scholar · View at Scopus
  12. H. H. Sherief, “State space formulation for generalized thermoelasticity with one relaxation time including heat sources,” Journal of Thermal Stresses, vol. 16, pp. 163–180, 1993. View at Google Scholar
  13. T. He, X. Tian, and Y. P. Shen, “State space approach to one-dimensional thermal shock problem for a semi-infinite piezoelectric rod,” International Journal of Engineering Science, vol. 40, no. 10, pp. 1081–1097, 2002. View at Publisher · View at Google Scholar · View at Scopus
  14. M. A. Ezzat, “State space approach to solids and fluids,” Canadian Journal of Physics, vol. 86, no. 11, pp. 1241–1250, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. H. M. Youssef and A. A. El-Bary, “Generalized thermoelastic infinite layer subjected to ramp-type thermal and mechanical loading under three theories—State space approach,” Journal of Thermal Stresses, vol. 32, no. 12, pp. 1293–1309, 2009. View at Google Scholar · View at Scopus
  16. K. A. Elsibai and H. M. Youssef, “State-space approach to vibration of gold nano-beam induced by ramp type heating without energy dissipation in femtoseconds scale,” Journal of Thermal Stresses, vol. 34, no. 3, pp. 244–263, 2011. View at Publisher · View at Google Scholar · View at Scopus
  17. S. Deswal, S. S. Sheoran, and K. K. Kalkal, “The effect of magnetic field and initial stress on fractional order generalized thermoelastic half-space,” Journal of Mathematics, vol. 2013, Article ID 489863, 11 pages, 2013. View at Publisher · View at Google Scholar
  18. M. A. Biot, Mechanics of Incremental Deformations, John Wiley & Sons, New York, NY, USA, 1965.
  19. A. Chattopadhyay, S. Bose, and M. Chakraborty, “Reflection of elastic waves under initial stress at a free surface: P and SV motion,” Journal of the Acoustical Society of America, vol. 72, no. 1, pp. 255–263, 1982. View at Google Scholar · View at Scopus
  20. A. Montanaro, “On singular surfaces in isotropic linear thermoelasticity with initial stress,” Journal of the Acoustical Society of America, vol. 106, no. 3 I, pp. 1586–1588, 1999. View at Publisher · View at Google Scholar · View at Scopus
  21. M. I. A. Othman and Y. Song, “Reflection of plane waves from an elastic solid half-space under hydrostatic initial stress without energy dissipation,” International Journal of Solids and Structures, vol. 44, no. 17, pp. 5651–5664, 2007. View at Publisher · View at Google Scholar · View at Scopus
  22. B. Singh, “Effect of hydrostatic initial stresses on waves in a thermoelastic solid half-space,” Applied Mathematics and Computation, vol. 198, no. 2, pp. 494–505, 2008. View at Publisher · View at Google Scholar · View at Scopus
  23. P. J. Chen and M. E. Gurtin, “On a theory of heat conduction involving two temperatures,” Zeitschrift für angewandte Mathematik und Physik, vol. 19, no. 4, pp. 614–627, 1968. View at Publisher · View at Google Scholar · View at Scopus
  24. P. J. Chen, M. E. Gurtin, and W. O. Williams, “A note on non-simple heat conduction,” Zeitschrift für angewandte Mathematik und Physik, vol. 19, pp. 969–970, 1968. View at Google Scholar
  25. P. J. Chen, M. E. Gurtin, and W. O. Williams, “On the thermodynamics of non-simple elastic materials with two temperatures,” Zeitschrift für angewandte Mathematik und Physik, vol. 20, no. 1, pp. 107–112, 1969. View at Publisher · View at Google Scholar · View at Scopus
  26. R. Quintanilla, “On existence, structural stability, convergence and spatial behavior in thermoelasticity with two temperatures,” Acta Mechanica, vol. 168, no. 1-2, pp. 61–73, 2004. View at Google Scholar · View at Scopus
  27. H. M. Youssef, “Theory of two-temperature-generalized thermoelasticity,” IMA Journal of Applied Mathematics, vol. 71, no. 3, pp. 383–390, 2006. View at Publisher · View at Google Scholar · View at Scopus
  28. H. M. Youssef and E. A. Al-Lehaibi, “State-space approach of two-temperature generalized thermoelasticity of one-dimensional problem,” International Journal of Solids and Structures, vol. 44, no. 5, pp. 1550–1562, 2007. View at Publisher · View at Google Scholar · View at Scopus
  29. H. M. Youssef and A. A. El-Bary, “Two-temperature generalized thermoelasticity with variable thermal conductivity,” Journal of Thermal Stresses, vol. 33, no. 3, pp. 187–201, 2010. View at Publisher · View at Google Scholar · View at Scopus
  30. J. C. Misra, N. C. Chattopadhyay, and A. Chakravorty, “Study of thermoelastic wave propagation in a half-space using GN theory,” Journal of Thermal Stresses, vol. 23, no. 4, pp. 327–351, 2000. View at Publisher · View at Google Scholar · View at Scopus
  31. G. Honig and U. Hirdes, “A method for the numerical inversion of Laplace transforms,” Journal of Computational and Applied Mathematics, vol. 10, no. 1, pp. 113–132, 1984. View at Google Scholar · View at Scopus
  32. G. C. Charles, Matrices and Linear Transformations, Addison-Wesley, Reading, Mass, USA.
  33. R. Churchill, Operational Mathematics, McGraw-Hill, New York, NY, USA, 1972.
  34. W. H. Weiskopf, “Stresses in soils under a foundation,” Journal of the Franklin Institute, vol. 239, no. 6, pp. 445–465, 1945. View at Google Scholar · View at Scopus