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Reflection of plane waves in magneto-micropolar thermoelastic medium with voids and one relaxation time due to gravity and two-temperature theory

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Abstract

The present model presents the reflection phenomena in a linear and homogenous micropolar thermoelastic isotropic medium with voids. The effects of gravity and magnetic field are investigated in the case of two-temperature theory. The studied problem is investigated, under Lord and Shulman (L–S) theory with one (delay) relaxation time, analytically with constant amplitudes. It is shown that there exist five reflected plane waves: longitudinal, shear, thermal and those due micropolar and voids waves. In addition, the values of the complex modulus of the reflection coefficients are visualized graphically to display the effects of gravity, two-temperature parameter, magnetic field, time, variant angles of incidence and micropolarity with voids. The present results are applicable in many fields such as earthquakes engineering, nuclear physics and manufacturing. It is found that the obtained results are significant.

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References

  1. H W Lord and Y Shulman Journal of Mechanics and Physics of Solids 15 299 (1967)

    ADS  Google Scholar 

  2. A E Green and A Lindsay Journal of Elasticity 2 1 (1972)

    Google Scholar 

  3. M I M Hilal and M I A Othman Multidiscipline Modeling Materials and Structures 14 65 (2018)

    Google Scholar 

  4. A N Sinha and S B Sinha Journal of Physics of the Earth 22 237 (1974)

    Google Scholar 

  5. S B Sinha and K A Elsibai Journal of Thermal Stresses 19 763 (1996)

    Google Scholar 

  6. A M El-Naggar, Z Kishka, A M Abd-Alla, I A Abbas, S M Abo-Dahab and M Elsagheer Journal of Computational and Theoretical Nanoscience 10 1408 (2013)

    Google Scholar 

  7. J N Sharma, V Kumar and D Chand Journal of Thermal Stresses 26 925 (2003)

    Google Scholar 

  8. A C Eringen Journal of Mathematics and Mechanics 15 909 (1966)

    MathSciNet  Google Scholar 

  9. A C Eringen, Springer-Verlag, Berlin (1999)

  10. M I A Othman, R S Tantawi and M I M Hilal Journal of Theoretical and Applied Mechanics 54 847 (2016)

    Google Scholar 

  11. M Marin Acta Mechanica 122 155 (1997)

    MathSciNet  Google Scholar 

  12. M Hassan, M. Marin, S Z Alamri and R Ellahi Heat Transfer Research 49 1837 (2018)

    Google Scholar 

  13. M I M Othman and M Marin Results in Physics 7 3863 (2017)

    ADS  Google Scholar 

  14. [14] M I A Othman, R S Tantawi, M I M Hilal, Journal of Thermal Stresses 39 751 (2016)

    Google Scholar 

  15. M I A Othman, R S Tantawi and M I M Hilal Applied Mathematics and Computation 276 468 (2016)

    Google Scholar 

  16. M I M Hilal, R S Tantawi and M I A Othman Journal of Ocean Engineering and Science 3 325 (2018)

    Google Scholar 

  17. J W Nunziato and S C Cowin Archive for Rational Mechanics and Analysis 72 175 (1979)

    ADS  MathSciNet  Google Scholar 

  18. S C Cowin and J W Nunziato Journal of Elasticity 13 125 (1983)

    Google Scholar 

  19. P Puri and S C Cowin Journal of Elasticity 15 167 (1985)

    Google Scholar 

  20. D A Ieşan Acta Mechanica 60 67 (1986)

    Google Scholar 

  21. M I A Othman and M I M Hilal Journal of Porous Media 21 865 (2018)

    Google Scholar 

  22. T J Bromwich The Proceedings of the London Mathematical Society 30 98 (1898)

    MathSciNet  Google Scholar 

  23. A E H Love (Cambridge University Press, London) (1965)

  24. M I A Othman, M I M Hilal and Y D Elmaklizi Mechanics and Mechanical Engineering 21 657 (2017)

    Google Scholar 

  25. P J Chen and M E Gurtin Journal of Applied Mathematics and Physics 19 614 (1968)

    Google Scholar 

  26. P Puri and P M Jordan International Journal of Engineering Science 44 1113 (2006)

    MathSciNet  Google Scholar 

  27. W E Warren and P J Chen Acta Mechanica 16 21 (1973)

    Google Scholar 

  28. H M Youssef IMA Journal of Applied Mathematics 71 383 (2006)

    ADS  MathSciNet  Google Scholar 

  29. M I A Othman and M I M Hilal Journal of Mechanical Science & Technology 29 3739 (2015)

    Google Scholar 

  30. L Knopoff Journal of Geophysical Research 60 441 (1955)

    ADS  Google Scholar 

  31. M I A Othman, R S Tantawi and M I M Hilal Multidiscipline Modeling Materials and Structures 15 418 (2019)

    Google Scholar 

  32. M I M Hilal, Journal of the Brazilian Society of Mechanical Sciences and Engineering 41 447 (2019)

    Google Scholar 

  33. M M Bahatti, A Zeeshan, D Tripathi and R Ellahi Indian Journal of Physics, 92 423 (2018)

    ADS  Google Scholar 

  34. R Jhorar, D Tripathi, M M Bahatti and R Ellahi Indian Journal of Physics, 92 1229 (2018)

    ADS  Google Scholar 

  35. F Hussain, R Ellahi and A Zeeshan Applied Sciences, 8 1229 (2018)

    Google Scholar 

  36. M Hassan, M Marin, A Alsharif and R Ellahi Physics Letters A, 382 2749 (2018)

    ADS  MathSciNet  Google Scholar 

  37. S Z Alamri, A A Khan, M Azeez and R Ellahi Physics Letters A, 383 276 (2019)

    ADS  MathSciNet  Google Scholar 

  38. M A Yousif, H F Ismael, T Abbas and R Ellahi Heat Transfer Research, 50 649 (2019)

    Google Scholar 

  39. R Ellahi, S M Sait, N Shehzad and N Mobin Symmetry, 11 1038 (2019)

    Google Scholar 

  40. R Ellahi Applied Mathematical Modelling, 37 1451 (2013)

    MathSciNet  Google Scholar 

  41. M M Bahatti, A Zeeshan and R Ellahi Pramana Journal of Physics, 89 48 (2017)

    ADS  Google Scholar 

  42. A C Eringen International Journal of Engineering Science 22 1113 (1984)

    Google Scholar 

  43. R S Dhaliwal and A Singh, Hindustan Publication Corporation, New Delhi, India (1980)

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Basic Sciences, Faculty of Engineering, Sinai University, Al-Arish, Egypt

    Mohamed I. M. Hilal & S. A. Hanoura

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

    Mohamed I. M. Hilal & Elsayed M. Abd-Elaziz

Authors
  1. Mohamed I. M. Hilal
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  2. Elsayed M. Abd-Elaziz
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  3. S. A. Hanoura
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Correspondence to Mohamed I. M. Hilal.

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Hilal, M.I.M., Abd-Elaziz, E.M. & Hanoura, S.A. Reflection of plane waves in magneto-micropolar thermoelastic medium with voids and one relaxation time due to gravity and two-temperature theory. Indian J Phys 95, 915–924 (2021). https://doi.org/10.1007/s12648-020-01772-w

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  • DOI: https://doi.org/10.1007/s12648-020-01772-w

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