Skip to main content
SpringerLink
Log in

Influence of the gravitational field on a piezothermoelastic rotating medium with G-L theory

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract.

In the present paper, two different theories (coupled theory and Green-Lindsay theory with two relaxation times) are applied to study the deformation of a generalized piezothermoelastic rotating medium under the influence of gravity. The normal mode analysis is used to obtain the expressions for the displacement components, the temperature, the stress, the stress components, the electric potential and the electric displacements. Numerical results for the field quantities are given in the physical domain and illustrated graphically. Comparisons are made with the results predicted by coupled and Green-Lindsay theories in the presence and absence of rotation as well as of gravity.

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

Similar content being viewed by others

References

  1. T. Jana, E. Jiri, K. Erwin, P. Jana, Fundamentals of Piezoelectric Sensorics (Springer-Verlag, Berlin, Heidelberg, 2010)

  2. J. Curie, P. Curie, C. R. Acad. Sci. Bull. Soc. Minéral. 3, 294 (1880)

    Google Scholar 

  3. W.P. Mason, Piezoelectric Crystals and their Application to Ultrasonics (D. Van Nostrand Co. Inc., New York, 1950)

  4. M. Redwood, J. Acoust. Soc. Am. 33, 527 (1961)

    Article  ADS  Google Scholar 

  5. T. Chen, Proc. R. Soc. London A 454, 873 (1971)

    Article  ADS  Google Scholar 

  6. A.N. Abd-Alla, F.A. Alsheikh, A.Y. Al-Hossain, Meccanica 47, 731 (2012)

    Article  MathSciNet  Google Scholar 

  7. A.N. Abd-Alla, F.A. Alsheikh, Arch. Appl. Mech. 79, 843 (2009)

    Article  ADS  Google Scholar 

  8. R.D. Mindlin, Int. J. Solids Struct. 10, 625 (1974)

    Article  Google Scholar 

  9. W. Nowacki, J. Thermal Stresses 1, 171 (1978)

    Article  MathSciNet  Google Scholar 

  10. D.S. Chandrasekharaiah, Acta Mech. 71, 39 (1988)

    Article  Google Scholar 

  11. M.L. Dunn, J. Appl. Phys. 73, 5131 (1993)

    Article  ADS  Google Scholar 

  12. J.N. Sharma, M. Kumar, Indian J. Eng. Mater. Sci. 7, 434 (2000)

    Google Scholar 

  13. H.M. Youssef, E. Bassiouny, Comput. Methods Sci. Technol. 14, 55 (2008)

    Article  Google Scholar 

  14. A.H. Akbarzadeh, M.H. Babaei, Z.T. Chen, Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 225, 2537 (2011)

    Article  Google Scholar 

  15. F.A. Alshaikh, Appl. Math. 3, 819 (2012)

    Article  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  17. H.W. Lord, Y. Shulman, J. Mech. Phys. Solids 15, 299 (1967)

    Article  ADS  Google Scholar 

  18. A.E. Green, K.A. Lindsay, J. Elasticity 1, 1 (1972)

    Article  Google Scholar 

  19. M.I.A. Othman, S.M. Said, Int. J. Thermophys. 33, 1082 (2012)

    Article  ADS  Google Scholar 

  20. D.S. Chandrasekharaiah, K.R. Srikantiah, Acta Mech. 50, 211 (1984)

    Article  Google Scholar 

  21. M. Schoenberg, D. Censor, Quart. Appl. Math. 31, 115 (1973)

    Google Scholar 

  22. M.I.A. Othman, Int. J. Solids Struct. 41, 2939 (2004)

    Article  Google Scholar 

  23. J.N. Sharma, D. Thakur, J. Sound Vibrat. 296, 871 (2006)

    Article  ADS  Google Scholar 

  24. J.N. Sharma, V. Walia, S.K. Gupta, Int. J. Mech. 50, 433 (2008)

    Article  Google Scholar 

  25. X.-L. Peng, X.-F. Li, Int. J. Mech. Sci. 60, 84 (2012)

    Article  Google Scholar 

  26. T. Hayat, S. Mumtaz, R. Ellahi, Acta Mech. Sin. 19, 235 (2003)

    Article  ADS  Google Scholar 

  27. T. Hayat, R. Ellahi, S. Asghar, A.M. Siddiqui, Appl. Math. Model. 28, 591 (2004)

    Article  Google Scholar 

  28. T. Hayat, R. Ellahi, S. Asghar, Math. Comput. Model. 40, 173 (2004)

    Article  MathSciNet  Google Scholar 

  29. T. Hayat, R. Ellahi, S. Asghar, Chem. Eng. Commun. 194, 37 (2007)

    Article  Google Scholar 

  30. T. Hayat, R. Ellahi, S. Asghar, Chem. Eng. Commun. 195, 958 (2008)

    Article  Google Scholar 

  31. R. Ellahi, S. Asghar, Int. J. Fluid Mech. Res. 34, 548 (2007)

    Article  Google Scholar 

  32. T.J.J.A. Bromwich, Proc. London Math. Soc. 30, 98 (1898)

    Article  MathSciNet  Google Scholar 

  33. A.E.H. Love, Some Problems of Geodynamics (Dover, New York, 1911)

  34. S.N. De, P.R. Sengurta, J. Acoust. Soc. Am. 55, 919 (1974)

    Article  ADS  Google Scholar 

  35. S.N. De, P.R. Sengurta, Gerlands Beitr. Geophys. (Leipzig) 85, 311 (1976)

    Google Scholar 

  36. M.I.A. Othman, S.Y. Atwa, A.W. Elwan, J. Comput. Theor. Nanosci. 13, 2827 (2016)

    Article  Google Scholar 

  37. M.I.A. Othman, J.D. Elmaklizi, S.M. Said, Int. J. Thermophys. 34, 521 (2013)

    Article  ADS  Google Scholar 

  38. M.I.A. Othman, S.M. Said, Int. J. Thermophys. 33, 160 (2012)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Taif University 888, Taif, Saudi Arabia

    Mohamed I.A. Othman

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

    Mohamed I.A. Othman & Ethar A.A. Ahmed

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

    You can also search for this author in PubMed Google Scholar

  2. Ethar A.A. Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamed I.A. Othman.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Othman, M., Ahmed, E. Influence of the gravitational field on a piezothermoelastic rotating medium with G-L theory. Eur. Phys. J. Plus 131, 358 (2016). https://doi.org/10.1140/epjp/i2016-16358-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2016-16358-1

Search

Navigation