Table of Contents
Journal of Thermodynamics
Volume 2014, Article ID 134276, 10 pages
http://dx.doi.org/10.1155/2014/134276
Research Article

Effect of Initial Stress on the Propagation Characteristics of Waves in Fiber-Reinforced Transversely Isotropic Thermoelastic Material under an Inviscid Liquid Layer

1Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana 136119, India
2University Institute of Engg. & Tech., Kurukshetra University, Kurukshetra, Haryana 136119, India
3Department of Mathematics, Deen Bandhu Chotu Ram Uni. of Sc. & Tech., Sonipat, Haryana 131027, India

Received 24 May 2014; Accepted 17 July 2014; Published 26 August 2014

Academic Editor: Felix Sharipov

Copyright © 2014 Rajneesh Kumar et al. 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. A. J. M. Spencer, Deformation of Fibre-reinforced Materials, University of Oxford, Clarendon, Va, USA, 1941.
  2. A. J. Belfield, T. G. Rogers, and A. J. M. Spencer, “Stress in elastic plates reinforced by fibres lying in concentric circles,” Journal of the Mechanics and Physics of Solids, vol. 31, no. 1, pp. 25–54, 1983. View at Publisher · View at Google Scholar · View at Scopus
  3. A. C. Pipkin, “Finite deformations of ideal fiber-reinforced composites,” in Composites Materials, G. P. Sendeckyj, Ed., vol. 2 of Mechanics of Composite Materials, pp. 251–308, Academic Press, New York, NY, USA, 1973. View at Google Scholar
  4. P. R. Sengupta and S. Nath, “Surface waves in fibre-reinforced anisotropic elastic media,” Indian Academy of Sciences, Sadhana Proceedings, vol. 26, pp. 363–370, 2001. View at Google Scholar
  5. 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 Publisher · View at Google Scholar · View at Scopus
  6. R. S. Dhaliwal and H. H. Sherief, “Generalized thermoelasticity for anisotropic media,” Quarterly of Applied Mathematics, vol. 38, no. 1, pp. 1–8, 1980/81. View at Google Scholar · View at MathSciNet · View at Scopus
  7. A. U. Erdem, “Heat Conduction in fiber-reinforced rigid bodies,” 10 Ulusal Ist Bilimi ve Tekmgi Kongrest (ULIBTK), 6–8 Eylul, Ankara, Turkey, 1995.
  8. R. Kumar and R. R. Gupta, “Study of wave motion in an anisotropic fiber-reinforced thermoelastic solid,” Journal of Solid Mechanics, vol. 2, no. 1, pp. 91–100, 2010. View at Google Scholar · View at Scopus
  9. P. Chadwick and L. T. C. Seet, “Wave propagation in a transversely isotropic heat-conducting elastic material,” Mathematika, vol. 17, pp. 255–274, 1970. View at Google Scholar · View at MathSciNet
  10. H. Singh and J. N. Sharma, “Generalized thermoelastic waves in transversely isotropic media,” Journal of the Acoustical Society of America, vol. 77, pp. 1046–1053, 1985. View at Publisher · View at Google Scholar
  11. B. Singh, “Wave propagation in an anisotropic generalized thermoelastic solid,” Indian Journal of Pure and Applied Mathematics, vol. 34, no. 10, pp. 1479–1485, 2003. View at Google Scholar · View at Scopus
  12. P. Chadwick, Progress in Solid Mechanics, vol. 1, North-Holland, Amsterdam, The Netherlands, 1960, edited by R. Hill, I. N. Sneddon.
  13. P. Chadwick and D. W. Windle, “Propagation of Rayleigh waves along isothermal and insulated boundaries,” Proceedings of the Royal Society of America, vol. 280, pp. 47–71, 1964. View at Google Scholar · View at MathSciNet
  14. J. N. Sharma and H. Singh, “Thermoelastic surface waves in a transversely isotropic half space with thermal relaxations,” Indian Journal of Pure and Applied Mathematics, vol. 16, no. 10, pp. 1202–1219, 1985. View at Google Scholar · View at MathSciNet
  15. A. Montanaro, “On singular surfaces in isotropic linear thermoelasticity with initial stress,” Journal of the Acoustical Society of America, vol. 106, no. 3, pp. 1586–1588, 1999. View at Publisher · View at Google Scholar · View at Scopus
  16. J. Wang and P. Slattery, “Thermoelasticity without energy dissipation for initially stressed bodies,” International Journal of Mathematics and Mathematical Sciences, vol. 31, no. 6, pp. 329–337, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. D. Ieşan, “A theory of prestressed thermoelastic Cosserat continua,” Journal of Applied Mathematics and Mechanics, vol. 88, no. 4, pp. 306–319, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. K. Ames and B. Straughan, “Continuous dependence results for initially prestressed thermoelastic bodies,” International Journal of Engineering Science, vol. 30, no. 1, pp. 7–13, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. J. Wang, R. S. Dhaliwal, and S. R. Majumdar, “Some theorems in the generalized theory of thermoelasticity for prestressed bodies,” Indian Journal of Pure and Applied Mathematics, vol. 28, no. 2, pp. 267–276, 1997. View at Google Scholar · View at MathSciNet · View at Scopus
  20. M. Marin and C. Marinescu, “Thermoelasticity of initially stressed bodies, asymptotic equipartition of energies,” International Journal of Engineering Science, vol. 36, no. 1, pp. 73–86, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. V. V. Kalinchuk, T. I. Belyankova, Y. E. Puzanoff, and I. A. Zaitseva, “Some dynamic properties of the nonhomogeneous thermoelastic prestressed media,” The Journal of the Acoustical Society of America, vol. 105, no. 2, p. 1342, 1999. View at Google Scholar
  22. 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
  23. B. Singh, “Wave propagation in an initially stressed transversely isotropic thermoelastic solid half-space,” Applied Mathematics and Computation, vol. 217, no. 2, pp. 705–715, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  24. M. I. A. Othman, S. M. Said, and N. Sarker, “Effect of hydrostatic initial stress on a fiber-reinforced thermoelastic medium with fractional derivative heat transfer,” Multidiscipline Modeling in Materials and Structures, vol. 9, no. 3, pp. 410–426, 2013. View at Publisher · View at Google Scholar
  25. A. M. Abd-Alla, S. M. Abo-Dahab, and A. Al-Mullise, “effects of rotation and gravity field on surface waves in fibre-reinforced thermoela stic media under four theories,” Journal of Applied Mathematics, vol. 2013, Article ID 562369, 10 pages, 2013. View at Publisher · View at Google Scholar
  26. M. I. A. Othman and S. Y. Atwa, “Effect of rotation on a fiber-reinforced thermo-elastic under Green-Naghdi theory and influence of gravity,” Meccanica, vol. 49, no. 1, pp. 23–36, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  27. I. A. Abbas, “Generalized magneto-thermoelastic interaction in a fiber-reinforced anisotropic hollow cylinder,” International Journal of Thermophysics, vol. 33, no. 3, pp. 567–579, 2012. View at Publisher · View at Google Scholar · View at Scopus
  28. I. A. Abbas, “A GN model for thermoelastic interaction in an unbounded fiber-reinforced anisotropic medium with a circular hole,” Applied Mathematics Letters, vol. 26, no. 2, pp. 232–239, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. I. A. Abbas and A. Zenkour, “Two-temperature generalized thermoelastic interaction in an infinite fiber-reinforced anisotropic plate containing a circular cavity with two relaxation times,” Journal of Computational and Theoretical Nanoscience, vol. 11, no. 1, pp. 1–7, 2014. View at Publisher · View at Google Scholar
  30. I. A. Abbas and M. I. A. Othman, “Generalized thermoelastic interaction in a fiber-reinforced anisotropic half-space under hydrostatic initial stress,” Journal of Vibration and Control, vol. 18, no. 2, pp. 175–182, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. W. M. Ewing, W. S. Jardetzky, and F. Press, Elastic Waves in Layered Media, McGraw-Hill, New York, NY, USA, 1957. View at MathSciNet
  32. H. Kolsky, Stress Waves in Solids, Clarendon Press, Dover, New York, NY, USA, 1963.
  33. M. A. Ezzat, “Fundamental solution in generalized magneto-thermoelasticity with two relaxation times for perfect conductor cylindrical region,” International Journal of Engineering Science, vol. 42, no. 13-14, pp. 1503–1519, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus