Skip to main content
SpringerLink
Log in

Memory-dependent derivative effect on 2D problem of generalized thermoelastic rotating medium with Lord–Shulman model

  • Original Paper
  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

The model of two-dimensional plane waves is studied in a generalized thermoelastic medium under memory-dependent derivative in the Lord–Shulman model. The normal mode analysis is used to obtain the exact expressions for the temperature distribution, the displacement component and the thermal stress component. The resulting formulation is applied to a concrete problem that deals with a thick plate subjected to a time-dependent heat source on each face. According to the graphical representations, corresponding to the numerical results, the effect of the different kernel has studied different thermophysical quantities at different times. Moreover, graphs are drawn to show the influence of rotation in all the thermophysical quantities. Some three-dimensional figures also are drawn for a better understanding of thermophysical quantities in the different positions of the body. As per the author’s knowledge, the effect of rotation with the memory effect is not available in the literature till now. The differences for different kernel functions are also presented at different times.

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

Access this article

Log in via an institution

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. H W Lord and Y Shulman J. Mech. Phys. Solids15 299 (1967)

    Article  ADS  Google Scholar 

  2. M I A Othman J. Therm. Stress.25 1027 (2002)

    Article  Google Scholar 

  3. M I A Othman Multidicip. Model. Mater. Struct.1 231 (2005)

    Article  Google Scholar 

  4. M Marin, M I A Othman, I A Abbas J. Comput. Theor. Nanosci. 12 1594 (2015)

    Article  Google Scholar 

  5. K Diethelm The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type (Berlin: Springer) (2010)

    Book  Google Scholar 

  6. M Caputo Geophys. J. Int.13 529 (1967)

    Article  ADS  Google Scholar 

  7. M Caputo and M Fabrizio Progr. Fract. Differ. Appl. 1 73 (2015)

    Google Scholar 

  8. J L Wang and H F Li Comput. Math. Appl.62 1562 (2011)

    Article  MathSciNet  Google Scholar 

  9. M A Ezzat, A S El-Karamany and A A El-Bary Mech. Adv. Mater. Struct.23 545 (2016)

    Article  Google Scholar 

  10. S M Said Meccanica50 2077 (2015)

    Article  MathSciNet  Google Scholar 

  11. S Shaw and B Mukhopadhyay Acta Mech.228 2675 (2017)

    Article  MathSciNet  Google Scholar 

  12. S M Said Comput. Mater. Contin.52 1 (2016)

    Google Scholar 

  13. A Sur, P Pal and M Kanoria J Therm Stress41 973 (2018)

    Article  Google Scholar 

  14. A Sur and M Kanoria Thin-Walled Struct.126 85 (2018)

    Article  Google Scholar 

  15. P Purkait, A Sur and M Kanoria Int. J. Adv. Appl. Math. Mech.5 28 (2017)

    MathSciNet  Google Scholar 

  16. N Sarkar, D Ghosh and A Lahiri Mech. Adv. Mater. Struct.26 957 (2019)

    Article  Google Scholar 

  17. M K A Zaini, M H Lai, Md R Islam, K S Lim, H Ahmad Ind. J. Phys. 92 1045 (2018)

    Article  Google Scholar 

  18. S M Said Multidiscip. Model. Mater. Struct. 11 297 (2015)

    Article  Google Scholar 

  19. R Ellahi, A Zeeshan, F Hussain and T Abbas Coatings8 422 (2018)

    Article  Google Scholar 

  20. S Roy Chaudhuri and L Debnath Int. J. Eng. Sci.21 155 (1983)

    Article  Google Scholar 

  21. S H Kordkheili and R Naghdabadi Compos. Struct.79 508 (2007)

    Article  Google Scholar 

  22. M Marin and A Oechsner Contin Mech Thermodyn. 29 1365 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  23. M Hassan, M Marin, A Alsharif and R Ellahi (2018) Phys. Lett. Sect. A Gen. At. Solid State Phys.382 2749

    Google Scholar 

  24. M I A Othman and B Singh Int. J. Solids and Struct. 44 2748 (2007)

    Article  Google Scholar 

  25. F S Bayones and A M Abd-Alla Results Phys.7 2941 (2017)

    Article  ADS  Google Scholar 

  26. M Marin Acta Mech. 122 155 (1997)

    Article  MathSciNet  Google Scholar 

  27. M Schoenberg and D Censor Q. Appl. Math.31 115 (1973)

    Article  Google Scholar 

  28. M A Ezzat and M I A Othman Int. J. Eng. Sci.38 107 (2000)

    Article  Google Scholar 

  29. M A Biot J. Appl. Phys.27 240 (1956)

    Article  ADS  MathSciNet  Google Scholar 

  30. M I A Othman and N H Sweilam Can. J. Phys.80 697 (2002)

    Article  ADS  Google Scholar 

  31. R Ellahi, M H Tariq, M Hassan and K Vafai, J. Mol. Liq.229 339 (2017)

    Article  Google Scholar 

  32. R Jhorar, D Tripathi, M M Bhatti and R Ellahi Ind. J. Phys. 92 1229 (2018)

    Article  Google Scholar 

  33. M A Yousif, H F Ismael, T Abbas and R Ellahi Heat Transf. Res.50 649 (2019)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Mohamed I. A. Othman

  2. Department of Mathematics, Basirhat College, 24pgs(N), Basirhat, 743412, India

    Sudip Mondal

Authors
  1. Mohamed I. A. Othman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sudip Mondal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamed I. A. Othman.

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

Othman, M.I.A., Mondal, S. Memory-dependent derivative effect on 2D problem of generalized thermoelastic rotating medium with Lord–Shulman model. Indian J Phys 94, 1169–1181 (2020). https://doi.org/10.1007/s12648-019-01548-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12648-019-01548-x

Keywords

PACS Nos.

Search

Navigation