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Rotational effect on Rayleigh, Love and Stoneley waves in fibre-reinforced anisotropic general viscoelastic media of higher and fraction orders with voids

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Abstract

In this paper, we investigated the propagation of surface waves in a rotating fibre-reinforced viscoelastic anisotropic media of a higher order and fraction orders of nth order including time rate of strain with voids. The general surface wave speed is derived to study the effect of rotation and voids on surface waves. Particular cases for Stoneley, Love and Rayleigh waves are also discussed. The results obtained in this investigation are more general in the sense that some earlier published results are obtained from our result as special cases. In order zero our results are well agreeing with classical results. Also by neglecting the reinforced elastic parameters and voids the results reduce to well known isotropic medium. Comparison was made with the results obtained in the presence and absence of rotation and parameters for fibre-reinforced of the material medium. It is observed that Love wave remains unaffected with respect to rotation and voids. It is also observed that, surface waves cannot propagate in a fast rotating medium. Numerical results are given and illustrated graphically.

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References

  1. K. E. Bullen, An introduction to the theory of seismology, Cambridge University press, London (1965) 85–99.

    Google Scholar 

  2. W. M. Ewing and W. S. Jardetzky, Elastic waves in layered media, New York, Toronto, London: McGraw Hill Press F (1957) 348–350.

    MATH  Google Scholar 

  3. L. Rayleigh, On wave propagation along the plane surface of an elastic solid, Proc. London. Math. Soc., 17 (1885) 4–11.

    Article  MATH  Google Scholar 

  4. R. Stoneley, The elastic waves at the surface of separation of two solids, Proc. R. Soc. London, A106 (1924) 416–420.

    Article  Google Scholar 

  5. D. P. Acharya and P. R. Sengupta, Magneto-thermo-elastic surface waves in initially stressed conducting media, Acta-Geophys. Polon, A26 (1978) 299–311.

    Google Scholar 

  6. K. C. Pal and P. R. Sengupta, Surface waves in visco-elastic media of general type in the presence of thermal field and gravity, Proc. Indian Natl. Sci. Acad, A53 (1987) 353–372.

    Google Scholar 

  7. P. R. Sengupta and S. Nath. Surface waves in fibre-reinforced anisotropic elastic media, Sadhana, 26 (2001) 363–370.

    Article  Google Scholar 

  8. A. J. Belfield, T. G. Rogers and A. J. M. Spencer, Stress in elastic plates reinforced by fibre lying in concentric circles, J. Mech. Phys. Solids, 31 (1983) 25–54.

    Article  MATH  Google Scholar 

  9. M. Schoenberg and D. Censor, Elastic waves in rotating media, Quart. Appl. Math., 31 (1973) 115–125.

    MATH  Google Scholar 

  10. K. Sapan and R. C. Samaland, Surface wave propagation in fiber-reinforced anisotropic elastic layer between liquid saturated porous half space and uniform liquid layer, ActaGeophysica, 59 (3) (2011) 470–482.

    Google Scholar 

  11. B. Singh, Wave propagation in thermally conducting linear bre-reinforced composite materials, Arch Appl. Mech., 75b (2006) 513–520.

    Article  Google Scholar 

  12. R. Kakar, S. Kakar and K. Kaur, Rayleigh, Love and Stoneley waves in fibre-reinforced, anisotropic, viscoelastic media of higher order under gravity, International Journal of Physical and Mathematical Sciences, 4 (1) (2013) 53–61.

    Google Scholar 

  13. A. M. Abd-Alla, T. A. Nofal, S. M. Abo-Dahab and A. Al-Mullise, Surface waves propagation in fibre-reinforced anisotropic elastic media subjected to gravity field, Int J. Phys. Sci., 8 (14) (2013) 574–584.

    Google Scholar 

  14. A. Chattopadhyay, R. L. K. Venkateswarlu and S. Saha, Reflection of quasi-P and quasi-SV waves at the free and rigid boundaries of a fibre-reinforced medium, Sãdhanã, 27 (2002) 613–630.

    Google Scholar 

  15. B. Singh and S. J. Singh, Reflection of plane waves at the free surface of a fibre-reinforced elastic half space, Sãdhanã, 29 (2004) 249–257.

    MATH  Google Scholar 

  16. A. M. Abd-Alla, S. M. Abo-Dahab and A. Al-Mullise, Effects of rotation and gravity field on surface waves in Fiberreinforced thermoelastic media under four theories, Journal of Applied Mathematics (2013) 1–20.

    Google Scholar 

  17. B. Singh, Wave propagation in an incompressible transversely isotropic fibre-reinforced elastic media, Archive of Applied Mechanics, 77 (2007) 253–258.

    Article  MATH  Google Scholar 

  18. J. W. Nunziato and S. C. Cowin, A nonlinear theory of elastic materials with voids, Archive for Rational Mechanics and Analysis, 72 (2) (1979) 175–201.

    Article  MATH  MathSciNet  Google Scholar 

  19. S. C. Cowin and J. W. Nunziato, Linear elastic materials with voids, Journal of Elasticity, 13 (2) (1983) 125–147.

    Article  MATH  Google Scholar 

  20. P. Puri and S. C. Cowin, Plane waves in linear elastic materials with voids, Journal of Elasticity, 15 (2) (1985) 167–183.

    Article  MATH  Google Scholar 

  21. D. Iesan, A theory of thermoelastic materials with voids, Acta Mechanica, 60 (1-2) (1986) 67–89.

    Article  Google Scholar 

  22. B. Singh and R. Pal, Surface wave propagation in a generalized thermoelastic material with voids, Applied Mathematics, 2 (2011) 521–526.

    Article  MathSciNet  Google Scholar 

  23. K. C. Pal and P. R. Sengupta, Surface waves in visco-elastic media of general type in the presence of thermal field and gravity, Proc. Indian Natl. Sci. Acad., A53 (1987) 353–372.

    Google Scholar 

  24. R. Kakar, S. Kakar and K. K. Rayleigh, Love and Stoneley waves in fibre-reinforced, anisotropic, viscoelastic media of higher order under gravity, International Journal of Physical and Mathematical Sciences, 4 (1) (2013) 53–61.

    Google Scholar 

  25. S. M. Abo-Dahab, Analytic solution for the secular equation of gravity and magnetic field variation on propagation of surface waves in fibre-reinforced anisotropic thermoelastic solid with hydrostatic initial stress and two relaxation times, J. Comput. & Theoret. Nanoscience, 11 (12) (2014) 2545–2563.

    Article  Google Scholar 

  26. S. M. Abo-Dahab and E. Edfawy, Secular equation of magnetic field and gravity variation on propagation of surface waves in fibre-reinforced anisotropic thermoelastic solid with two relaxation times, J. Comput. & Theoret. Nanoscience, 11 (11) (2014) 2339–2355.

    Article  Google Scholar 

  27. A. M. Abd-Alla, S. M. Abo-Dahab and F. S. Bayones, Wave propagation in fibre-reinforced anisotropic thermoelastic medium subjected to gravity field, Structural Engineering and Mechanics, 53 (2015) 277–296.

    Article  Google Scholar 

  28. S. M. Abo-Dahab, Propagation of Stoneley waves in magneto-thermoelastic materials with voids and two relaxation times, J. Vib. & Control (2014).

    Google Scholar 

  29. S. M. Abo-Dahab and A. M. Abd-Alla, Effects of voids and rotation on plane waves in generalized thermoelasticity, Journal of Mechanical Science and Technology, 27 (2014) 3607–3614.

    Article  Google Scholar 

  30. A. M. Abd-Alla, S. M. Abo-Dahab and T. A. Al-Thamali, Propagation of Rayleigh waves in a rotating orthotropic material elastic half-space under initial stress and gravity, Journal of Mechanical Science and Technology, 26 (9) (2012) 281–2823.

    Article  Google Scholar 

  31. A. M. Abd-Alla and S. R. Mahmoud, Analytical solution of wave propagation in a non-homogeneous orthotropic rotating elastic media, Journal of Mechanical Science and Technology, 26 (3) (2012) 917–926.

    Article  Google Scholar 

  32. S. M. Abo-Dahab, A. M. Abd-Alla and I. H. El-Sirafy, Effect of gravity field, initial stress and rotation on the Swaves propagation in a non-homogeneous anisotropic medium with magnetic field, Journal of Mechanical Science and Technology, 28 (2014) 3003–3011.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Math. Dept., Faculty of Science, Taif University, Taif, 888, Saudi Arabia

    A. M. Abd-Alla & S. M. Abo-Dahab

  2. Math. Dept., Faculty of Science, Sohag University, Sohag, Egypt

    A. M. Abd-Alla

  3. Department of Mathematics, COMSATS, Institute of Information, Park Road, Chakshahzad, Islamabad, Pakistan

    Aftab Khan

  4. Math. Dept., Faculty of Science, SVU, Qena, 83523, Egypt

    S. M. Abo-Dahab

Authors
  1. A. M. Abd-Alla
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  2. Aftab Khan
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  3. S. M. Abo-Dahab
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Correspondence to Aftab Khan.

Additional information

Recommended by Associate Editor Seong Beom Lee

Aftab Khan started his carrier as a lecture at Postgraduate College and after that through public service exam he became Assistant and then Associate Professor and served as Principal at FG College. In 2003 he joined Karakuram International University Gilgit as Professor and served as Chairman Department of Mathematics and Dean faculty of sciences. In 2008 he joined COMSATS, Institute of Information technology, Chakshahzad, Park Road, Islamabad, Pakistan as a Professor and serving as Chairman of the department.

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Abd-Alla, A.M., Khan, A. & Abo-Dahab, S.M. Rotational effect on Rayleigh, Love and Stoneley waves in fibre-reinforced anisotropic general viscoelastic media of higher and fraction orders with voids. J Mech Sci Technol 29, 4289–4297 (2015). https://doi.org/10.1007/s12206-015-0926-z

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  • DOI: https://doi.org/10.1007/s12206-015-0926-z

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