Skip to main content
SpringerLink
Log in

Mathematical model for a magneto-thermoelastic micropolar medium with temperature-dependent material moduli under the effect of mechanical strip load

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

A new model of equations of generalized thermoelasticity for an isotropic medium with mechanical properties that are dependent on temperature is established. The present problem is a generalization of the three-phase-lag model, Lord and Shulman's coupled theory. The elasticity modulus is a reference temperature function which is linear. Analytical expressions of the considered variables are obtained by using the Laplace–Fourier transforms technique. The results are analysed in a deeper manner by comparing them with unique cases of absence of the magnetic field, temperature-dependent properties of the body, and two types of mechanical loads. The most significant points are highlighted.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  1. Eringen, A.C.: Linear theory of micropolar elasticity. J. Math. Mech. 15, 909–923 (1966)

    MathSciNet  MATH  Google Scholar 

  2. Othman, M.I.A., Hasona, W.M., Abd-Elaziz, E.M.: Effect of rotation on micropolar generalized thermoelasticity with two-temperatures using a dual-phase-lag model. Can. J. Phys. 92(2), 149–158 (2014)

    Article  Google Scholar 

  3. Parfitt, V.R., Eringen, A.C.: Reflection of plane waves from a flat boundary of a micropolar elastic half-space. J. Acoust. Soc. Amer. 45, 1258–1272 (1971)

    Article  Google Scholar 

  4. Sur, A., Kanoria, M.: Fractional order two-temperature thermoelasticity with finite wave speed. Acta Mech. 223, 2685–2701 (2012)

    Article  MathSciNet  Google Scholar 

  5. Othman, M.I.A., Song, Y.Q.: Effect of thermal relaxation and magnetic field on generalized micropolar thermoelastic medium. J. Appl. Mech. Tech. Phys. 57(1), 108–116 (2016)

    Article  MathSciNet  Google Scholar 

  6. Othman, M.I.A., Song, Y.Q.: The effect of rotation on the reflection of magneto-thermoelastic waves under thermoelasticity without energy dissipation. Acta Mech. 184(1–4), 189–204 (2006)

    Article  Google Scholar 

  7. Othman, M.I.A., Khan, A., Jahangir, R., Jahangir, A.: Analysis on plane waves through magneto-thermoelastic microstretch rotating medium with temperature dependent elastic properties. Appl. Math. Model. 65, 535–548 (2019)

    Article  MathSciNet  Google Scholar 

  8. Shaw, S., Othman, M.I.A.: Characteristics of Rayleigh wave propagating in orthotropic magneto-thermoelastic half-space: An eigen function expansion method. Appl. Math. Model 67, 605–620 (2019)

    Article  MathSciNet  Google Scholar 

  9. Pal, P., Das, P., Kanoria, M.: Magneto-thermoelastic response in a functionally graded rotating medium due to a periodically varying heat source. Acta Mech. 226, 2103–2120 (2015)

    Article  MathSciNet  Google Scholar 

  10. Ezzat, M.A., Othman, M.I.A.: State space approach to generalized magneto-thermo-elasticity with thermal relaxation in a medium of perfect conductivity. J. Therm. Stress. 25(5), 409–429 (2002)

    Article  Google Scholar 

  11. Othman, M.I.A., Singh, B.: The effect of rotation on generalized micropolar thermo- elasticity for a half-space under five theories. Int. J. Solids Struct. 44, 2748–2762 (2007)

    Article  Google Scholar 

  12. Abbas, I.A., Kumar, R.: Deformation due to thermal source in micropolar generalized thermoelastic half-space by finite element method. J. Comput. Theor. Nanosci. 11(1), 185–190 (2014)

    Article  Google Scholar 

  13. Zhang, P., Wei, P., Li, Y.: Wave propagation through a micropolar slab sandwiched by two elastic half-spaces. J. Vib. Acoust. 138(4), 041008 (2016)

    Article  Google Scholar 

  14. Chandrasekharaiah, D.S.: Heat-flux dependent micropolar thermoelasticity. Int. J. Eng. Sci. 24(8), 1389–1395 (1986)

    Article  Google Scholar 

  15. Marin, M.: Some basic theorems in elastostatics of micropolar materials with voids. J. Comput. Appl. Math. 70(1), 115–126 (1996)

    Article  MathSciNet  Google Scholar 

  16. Marin, M.: Harmonic vibrations in thermoelasticity of microstretch materials. J. Vib. Acoustics, Trans. ASME, 132(4), (2010) Art. No. 044501.

  17. Vlase, S., Marin, M., Öchsner, A., Scutaru, M.L.: Motion equation for a flexible one-dimensional element used in the dynamical analysis of a multibody system. Contin. Mech. Thermody. 31(3), 715–724 (2019)

    Article  MathSciNet  Google Scholar 

  18. Lomakin, A.: The Theory of Elasticity of Non Homogeneous Bodies. Ncew (1976)

  19. Noda, N.: Thermal stresses in materials with temperature-dependent properties. Appl. Mech. Rev. 44(9), 383–397

  20. Othman, M.I.A.: State space approach to the generalized thermoelastic problem with temperature-dependent elastic moduli and internal heat sources. J. Appl. Mech. Tech. Phys. 52(4), 644–656 (2011)

    Article  MathSciNet  Google Scholar 

  21. Ailawalia, P., Sachdeva, S.K.: Internal heat source in a temperature dependent thermoelastic half space with microtemperatures. J. Comput. Appl. Mech. 49(2), 351–358 (2018)

    Google Scholar 

  22. Das, N.C., Lahiri, A.: Eigenvalue approach to three dimensional coupled thermo-elasticity in a rotating transversely isotropic medium. Tamsui Oxford J. Math. Sci. 25, 237–257 (2009)

    MathSciNet  MATH  Google Scholar 

  23. Youssef, H.M.: Two-dimensional thermal shock problem of fractional order generalized thermoelasticity. Acta Mech. 223, 1219–1231 (2012)

    Article  MathSciNet  Google Scholar 

  24. Othman, M.I.A., Eraki, E.E.M.: Generalized magneto-thermoelastic half-space with diffusion under initial stress using three-phase-lag model. Mech. Based. Des. Struct. and Mach. 45(2), 145–159 (2017).

  25. Othman, M.I.A., Said, S.M., Marin, M.: A novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium under the effect of gravity with three-phase-lag model. Int. J. Numer. Methods Heat Fluid Flow 29(12), 4788–4806 (2019).

  26. Othman, M.I.A., Alharbi, A.M., Al-Autabi, A.MKh.: Micropolar thermoelastic medium with voids under the effect of rotation concerned with 3PHL model. Geomech Eng. 21(5), 447–459 (2020)

    Google Scholar 

  27. Shaw, S., Mukhopadhyay, B.: Analysis of Rayleigh surface wave propagation in isotropic micropolar solid under three-phase-lag model of thermoelasticity. Eur. J. Comput. Mech. 24(2), 64–78 (2015)

    Article  Google Scholar 

  28. Othman, M.I.A., Elmaklizi, Y.D., Said, S.M.: Generalized thermoelastic medium with temperature dependent properties for different theories under the effect of gravity field. Int. J. Thermophys. 34(3), 521–537 (2013)

    Article  Google Scholar 

  29. Eringen, A.C.: Mechanics of Micromorphic Material. In: Cortler M., editor. Proc. Eleventh Int. Congress of Applied Mechanics. Munich Berlin: Springer (1964)

  30. Choudhuri, S.R.: On a thermoelastic three-phase-lag model. J. Therm. Stress. 30, 231–238 (2007)

    Article  Google Scholar 

  31. Othman, M.I.A., Said, S.M.: The effect of rotation on a fiber-reinforced medium under generalized magneto-thermoelasticity with internal heat source. Mech. Adv. Mater. Struct. 22(3), 168–183 (2015)

    Article  Google Scholar 

  32. Ezzat, M.A., El-Karamany, A., Samaan, A.A.: The dependence of the modulus of elasticity on reference temperature in generalized thermoelasticity with thermal relaxation. Appl. Math. Comput. 147(1), 169–189 (2004)

    MathSciNet  MATH  Google Scholar 

  33. Shaw, S., Mukhopadhyay, B.: Moving heat source response in micropolar half-space with two-temperature theory. Contin. Mech. Thermodyn. 25, 523–535 (2013)

    Article  MathSciNet  Google Scholar 

  34. Shaw, S., Mukhopadhyay, B.: Electromagnetic effects on Rayleigh surface wave in a homogeneous isotropic thermo-microstretch elastic half-space. J. Eng. Phys. Thermophys. 85(1), 229–238 (2012)

    Article  Google Scholar 

Download references

Acknowledgement

The authors thank Taif University Researchers Supporting Project Number (TURSP-2020/230), Taif University, Taif, Saudi Arabia.

Funding

Funding for this research came from "Taif University Researchers Supporting Project Number (TURSP-2020/230), Taif University, Taif, Saudi Arabia".

Author information

Authors and Affiliations

  1. Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia

    Amnah M. Alharbi

  2. Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt

    Samia M. Said & Mohamed I. A. Othman

  3. Department of Mathematics, Zagazig Higher Institute of Eng. and Tech, Zagazig, Egypt

    Elsayed M. Abd-Elaziz

Authors
  1. Amnah M. Alharbi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Samia M. Said
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Elsayed M. Abd-Elaziz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mohamed I. A. Othman
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Authors have contributed equally to this work and approved for publication.

Corresponding author

Correspondence to Mohamed I. A. Othman.

Ethics declarations

Conflict of interest

There is no conflict of interest declared by the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alharbi, A.M., Said, S.M., Abd-Elaziz, E.M. et al. Mathematical model for a magneto-thermoelastic micropolar medium with temperature-dependent material moduli under the effect of mechanical strip load. Acta Mech 232, 2331–2346 (2021). https://doi.org/10.1007/s00707-021-02941-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-021-02941-6

Search

Navigation