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Acta Mechanica Solida Sinica

, Volume 28, Issue 6, pp 682–692 | Cite as

Effect of Fractional Order Parameter on Thermoelastic Behaviors of Elastic Medium with Variable Properties

  • Yingze Wang
  • Dong Liu
  • Qian Wang
  • Jianzhong Zhou
Article

Abstract

This paper is concerned with the thermoelastic behaviors of an elastic medium with variable thermal material properties. The problem is in the context of fractional order heat conduction. The governing equations with variable thermal properties were established by means of the fractional order calculus. The problem of a half-space formed of an elastic medium with variable thermal material properties was solved, and asymptotic solutions induced by a sudden temperature rise on the boundary were obtained by applying an asymptotic approach. The propagations of thermoelastic wave and thermal wave, as well as the distributions of displacement, temperature and stresses were obtained and plotted. Variations in the distributions with different values of fractional order parameter were discussed. The results were compared with those obtained from the case of constant material properties to evaluate the effects of variable material properties on thermoelastic behaviors.

Key Words

generalized thermoelasticity fractional order heat conduction variable thermal material properties asymptotic solution thermal shock 

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References

  1. 1.
    Mitra, K., Kumar, S., Vddavarz, A. and Moallemi, M.K., Experimental evidence of hyperbolic heat conduction in processed meat. ASME Journal of Heat Transfer, 1995, 117(3): 568–573.CrossRefGoogle Scholar
  2. 2.
    Biot, M.A., Thermoelasticity and irreversible thermodynamics. Journal of Applied Physics, 1956, 27(3): 240–253.MathSciNetCrossRefGoogle Scholar
  3. 3.
    Lord, H.W. and Shulman, Y., A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids, 1967, 15(3): 299–309.CrossRefGoogle Scholar
  4. 4.
    Green, A.E. and Lindsay, K.A., Thermoelasticity. Journal of Elasticity, 1972, 2(1): 1–7.CrossRefGoogle Scholar
  5. 5.
    Green, A.E. and Naghd, P.M., Thermoelasticity without energy dissipation. Journal of Elasticity, 1993, 31(3): 189–208.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Chandrasekharaiah, D.S., Hyperbolic thermoelasticity: a review of recent literature. Applied Mechanics Reviews, 1998, 51(12): 705–729.CrossRefGoogle Scholar
  7. 7.
    Hetnarski, R.B. and Ignaczak, J., Generalized thermoelasticity. Journal of Thermal Stresses, 1999, 22(4–5): 451–476.MathSciNetzbMATHGoogle Scholar
  8. 8.
    Tian, X.G. and Shen, Y.P., Research progress in generalized thermoelastic problems. Advances in Mechanics, 2012, 42(1): 1–11.MathSciNetGoogle Scholar
  9. 9.
    Ezzat, M.A., El-Karamany, A.S. and Samaan, A.A., The dependence of the modulus of elasticity on reference temperature in generalized thermoelasticity with thermal relaxation. Applied Mathematics and Computation, 2004, 147(1): 169–189.MathSciNetCrossRefGoogle Scholar
  10. 10.
    Ezzat, M.A., El-Karamany, A.S. and Samaan, A.A., State-space formulation to generalized thermoviscoelasticity with thermal relaxation. Journal of Thermal Stresses, 2001, 24(9): 823–846.CrossRefGoogle Scholar
  11. 11.
    Youssef, H.M., Dependence of modulus of elasticity and thermal conductivity on reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity. Applied Mathematics and Mechanics, 2005, 26(4): 470–475.CrossRefGoogle Scholar
  12. 12.
    Aouadi, M., Generalized thermo-piezoelectric problems with temperature-dependent properties. International Journal of Solids and Structures, 2006, 43(21): 6347–6358.CrossRefGoogle Scholar
  13. 13.
    Othman, M.I.A. and Kumar, R., Reflection of magneto-thermoelasticity waves with temperature dependent properties in generalized thermoelasticity. International Communication in Heat and Mass Transfer, 2009, 36(5): 513–520.CrossRefGoogle Scholar
  14. 14.
    Allam, M.N., Elsibai, K.A. and Abouelregal, A.E., Magneto-thermoelasticity for an infinite body with a spherical cavity and variable material properties without energy dissipation. International Journal of Solids and Structures, 2010, 47(20): 2631–2638.CrossRefGoogle Scholar
  15. 15.
    Akbarzadeh, A.H., Babaei, M.H. and Chen, Z.T., Thermopiezoelectric analysis of a functionally graded piezoelectric medium. International Journal of Applied Mechanics, 2011, 3(1): 47–68.CrossRefGoogle Scholar
  16. 16.
    Xiong, Q.L. and Tian, X.G., Transient magneto-thermoelastic response for a semi-infinite body with voids and variable material properties during thermal shock. International Journal of Applied Mechanics, 2011, 3(4): 161–185.CrossRefGoogle Scholar
  17. 17.
    Wang, Y.Z., Zhang, X.B. and Liu, D., Generalized thermoelastic solutions for the axisymmetric plane strain problem. Scientia Sinica Physica, Mechanica & Astronomica, 2013, 43(8): 956–964.CrossRefGoogle Scholar
  18. 18.
    Wang, Y.Z., Zhang, X.B. and Liu, D., Asymptotic analysis of generalized thermoelasticity for axisymmetric plane strain problem with temperature-dependent material properties. International Journal of Applied Mechanics, 2013, 5(2): 1350023–20.CrossRefGoogle Scholar
  19. 19.
    Povstenko, Y.Z., Fractional heat conduction equation and associated thermal stress. Journal of Thermal Stresses, 2004, 28(1): 83–102.MathSciNetCrossRefGoogle Scholar
  20. 20.
    Youssef, H.M., Theory of fractional order generalized thermoelasticity. ASME Journal of Heat Transfer, 2010, 132(6): 061301–7.CrossRefGoogle Scholar
  21. 21.
    Sherief, H.H., El-Sayed, A.M.A. and Abd El-Latief, A.M., Fractional order theory of thermoelasticity. International Journal of Solids and Structures, 2010, 47(2): 269–275.CrossRefGoogle Scholar
  22. 22.
    Povstenko, Y.Z., Fractional cattaneo-type equations and generalized thermoelasticity. Journal of Thermal Stresses, 2011, 34(2): 97–114.CrossRefGoogle Scholar
  23. 23.
    Kothari, S. and Mukhopadhyay, S., A problem on elastic half space under fractional order theory of thermoelasticity. Journal of Thermal Stresses, 2010, 34(7): 724–739.CrossRefGoogle Scholar
  24. 24.
    Ezzat, M.A., El-karamany, A.S. and Ezzat, S.M., Two-temperature theory in magneto-thermoelasticity with fractional order dual-phase-lag heat transfer. Nuclear Engineering and Design, 2012, 252: 267–277.CrossRefGoogle Scholar
  25. 25.
    Youssef, H.M., State-space approach to fractional order two-temperature generalized thermoelastic medium subjected to moving heat source. Mechanics of Advanced Materials and Structures, 2013, 20(1): 47–60.CrossRefGoogle Scholar
  26. 26.
    Sherief, H.H. and Abd El-Latief, A.M., Effect of variable thermal conductivity on a half-space under the fractional order theory of thermoelasticity. International Journal of Mechanical Sciences, 2013, 74: 185–189.CrossRefGoogle Scholar
  27. 27.
    El-Karamany, A.S. and Ezzat, M.A., Thermal shock problem in generalized thermoviscoelasticity under four theories. International Journal of Engineering Science, 2004, 42: 649–671.MathSciNetCrossRefGoogle Scholar
  28. 28.
    Wang, Y.Z., Zhang, X.B. and Song, X.N., A unified generalized thermoelasticity solution for the transient thermal shock problem. Acta Mechanica, 2012, 223(4): 735–743.MathSciNetCrossRefGoogle Scholar
  29. 29.
    Balla, M., Analytical study of the thermal shock problem of a half-space with various thermoelastic models. Acta Mechanica, 1991, 89(1–4): 73–92.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2015

Authors and Affiliations

  • Yingze Wang
    • 1
  • Dong Liu
    • 1
  • Qian Wang
    • 1
  • Jianzhong Zhou
    • 2
  1. 1.Department of Energy and Power EngineeringJiangsu UniversityZhenjiangChina
  2. 2.Department of Mechanical EngineeringJiangsu UniversityZhenjiangChina

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