229
Views
14
CrossRef citations to date
0
Altmetric
Original Articles

Two-dimensional electromagneto-thermoelastic coupled problem under fractional order theory of thermoelasticity

, &
Pages 645-657 | Received 06 Nov 2017, Accepted 27 Dec 2017, Published online: 08 Feb 2018

References

  • M. A. Biot, “Thermoelasticity and irreversible thermodynamics,” J. Appl. Phys., vol. 27, pp. 240–253, 1956.
  • H. W. Lord, and Y. Shulman, “A generalized dynamical theory of thermoelasticity,” J. Mech. Phys. Solid, vol. 15, pp. 299–309, 1967.
  • A. E. Green, and K. A. Lindsany, “Thermoelasticity,” J. Elast., vol. 2, no. 1, pp. 1–7, 1972.
  • A. E. Green, and P. M. Naghdi, “A reexamination of the basic results of thermomechanics,” Proc. R. Soc. London, vol. 432, pp. 171–194, 1991.
  • A. E. Green, and P. M. Naghdi, “On undamped heat waves in an elastic solid,” J. Therm. Stresses, vol. 15, pp. 252–264, 1992.
  • A. E. Green, and P. M. Naghdi, “Thermoelasticity without energy dissipation,” J. Elast., vol. 31, pp. 189–208, 1993.
  • J. N. Sharma, and D. Chand, “Transient generalized magnetothermoelastic waves in a half space,” Int. J. Eng. Sci., vol. 26, no. 9, pp. 951–958, 1988.
  • D. S. Chandrasekharaiah, K. S. Srinath, and L. Debnath, “Magnetothermoelastic disturbances with thermal relaxation in a solid due to heat sources,” Comput. Math. Appl., vol. 15, no. 6–8, pp. 483–490, 1988.
  • H. H. Sherief, and M. A. Ezzat, “A problem in generalized magnetothermoelasticity for an infinitely long annular cylinder,” J. Eng. Math., vol. 34, pp. 387–402, 1998.
  • H. H. Sherief, and K. A. Helmy, “A two-dimensional problem for a half-space in magneto-thermoelasticity with thermal relaxation,” Int. J. Eng. Sci., vol. 40, pp. 587–604, 2002.
  • S. K. Roy Choudhuri, and G. Chatterjee Roy, “Temperature-rate dependent magneto-thermoelastic waves in a finitely conducting elastic half-space,” Comput. Math. Appl., vol. 19, no. 5, pp. 85–93, 1990.
  • M. A. Ezzat, and M. I. Othman, “Electromagneto-thermoelastic plane waves with two relaxation times in a medium of perfect conductivity,” Int. J. Eng. Sci., vol. 38, pp. 107–120, 2000.
  • M. A. Ezzat, M. I. Othman, and A. A. Smaan, “State space approach to two-dimensional electromagneto-thermoelastic problem with two relaxation times,” Int. J. Eng. Sci., vol. 39, pp. 1383–1404, 2001.
  • T. H. He, X. G. Tian, and Y. P. Shen, “Two-dimensional generalized thermal shock problem of a thick piezoelectric plate of infinite extent,” Int. J. Eng. Sci., vol. 40, pp. 2249–2264, 2002.
  • M. Aouadi, “Hybrid Laplace transform-finite element method to a generalized electromagneto- thermoelastic problem,” Appl. Math. Model., vol. 31, pp. 712–726, 2007.
  • M. Caputo, “Vibrations on an infinite viscoelastic layer with a dissipative memory,” J. Acoust. Soc. Am., vol. 56, pp. 897–904, 1974.
  • R. L. Bagley, and P. J. Torvik, “A theoretical basis for the application of fractional calculus to viscoelasticity,” J. Rheol., vol. 27, pp. 201–210, 1983.
  • R. C. Koeller, “Applications of fractional calculus to the theory of viscoelasticity,” J. Appl. Mech., vol. 51, pp. 299–307, 1984.
  • Y. A. Rossikhin, and M. V. Shitikova, “Applications of fractional calculus to dynamic problems of linear and nonlinear heredity mechanics of solids,” Appl. Mech. Rev., vol. 50, pp. 15–67, 1997.
  • Y. Povstenko, Fractional Thermoelasticity. Springer: New York, 2015.
  • Y. B. Ma, and T. H. He, “Dynamic response of a generalized piezoelectric thermoelastic problem under fractional order theory of thermoelasticity,” Mech. Adv. Mater. Struct., vol. 23, no. 10, pp. 1173–1180, 2016.
  • Y. B. Ma, and T. H. He, “Thermal shock dynamic response of an infinite body with a spherical cavity under fractional order theory of thermoelasticty,” Eng. Mech., vol. 7, pp. 31–38, 2016.
  • Y. B. Ma, and T. H. He, “The transient response of a functionally graded piezoelectric rod subjected to a moving heat source under fractional order theory of thermoelasticity,” Mech. Adv. Mater. Struct., vol. 24, no. 9, pp. 789–796, 2016.
  • Y. Z. Povstenko, “Thermoelasticity that uses fractional heat conduction equation,” J. Math. Sci., vol. 162, pp. 296–305, 2009.
  • Y. Z. Povstenko, “Fractional heat conduction and associated thermal stress,” J. Therm. Stresses, vol. 28, pp. 83–102, 2005.
  • Y. Z. Povstenko, “Fractional Cattaneo-type equations and generalized thermo-elasticity,” J. Therm. Stresses, vol. 34, pp. 97–114, 2011.
  • H. M. Youssef, “Theory of fractional order generalized thermoelasticity,” J. Heat Trans., vol. 132, no. 6, pp. 1–7, 2010.
  • H. M. Youssef, and E. A. Al-Lehaibi, “Fractional order generalized thermoelastic half-space subjected to ramp-type heating,” Mech. Res. Commun., vol. 37, no. 5, pp. 448–452, 2010.
  • H. H. Sherief, A. M. A. El-Sayed, and A. M. Abd El-Latief, “Fractional order theory of thermoelasticity,” Int. J. Solids Struct., vol. 47, no. 2, pp. 269–275, 2010.
  • K. S. Miller, and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley: New York, 1993.
  • Y. Povstenko, “Fractional heat conduction in a space with a source varying harmonically in time and associated thermal stresses,” J. Therm. Stresses, vol. 39, pp. 1442–1450, 2016.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.