Geomechanics and Engineering

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Reflection and propagation of plane waves at free surfaces of a rotating micropolar fibre-reinforced medium with voids

  • Anya, Augustine Igwebuike (Department of Mathematics, COMSATS University Islamabad, ParkRoad Chak Shahzad) ;
  • Khan, Aftab (Department of Mathematics, COMSATS University Islamabad, ParkRoad Chak Shahzad)
  • Received : 2018.10.11
  • Accepted : 2019.08.17
  • Published : 2019.08.30
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Abstract

The present paper seeks to investigate propagation and reflection of waves at free surfaces of homogeneous, anisotropic and rotating micropolar fibre-reinforced medium with voids. It has been observed that, in particular when P-wave is incident on the free surface, there exist four coupled reflected plane waves traveling in the medium; quasi-longitudinal displacement (qLD) wave, quasi-transverse displacement (qTD) wave, quasi-transverse microrotational wave and a wave due to voids. Normal mode Analysis usually called harmonic solution method is adopted in concomitant with Snell's laws and appropriate boundary conditions in determination of solution to the micropolar fibre reinforced modelled problem. Amplitude ratios which correspond to reflected waves in vertical and horizontal components are presented analytically. Also, the Reflection Coefficients are presented using numerical simulated results in graphical form for a particular chosen material by the help of Mathematica software. We observed that the micropolar fibre-reinforced, voids and rotational parameters have various degrees of effects to the modulation, propagation and reflection of waves in the medium. The study would have impact to micropolar fibre-reinforecd rotational-acoustic machination fields and future works about behavior of seismic waves.

Keywords

Acknowledgement

Supported by : COMSATS University Islamabad

References

  1. Abd-Alla, A.M., Abo-Dahab, S.M. and Khan, A. (2017), "Rotational effects on magneto-thermoelastic Stoneley, Love and Rayleigh waves in fibre-reinforced anisotropic general viscoelastic media of higher order", CMC, 53(1), 49-72.
  2. Baljeet, S. (2017), "Reflection of elastic waves from plane surface of a half-space with impedance boundary conditions", Geosci. Res., 2(4), 242-253. https://dx.doi.org/10.22606/gr.2017.24004.
  3. Biswas, P.K., Sengupta, P.R. and Debnath, L. (1996), "Axisymmetric problems of wave propagation under the influence of gravity in a micropolar viscolelastic Semi-infinite medium", Int. J. Math. Math. Sci., 19(4), 815-820. https://doi.org/10.1155/s0161171296001135.
  4. Chakraborty, N. and Singh, M.C. (2011), "Reflection and refraction of a plane thermoelastic wave at a solid-solid interface under perfect boundary condition, in presence of normal initial stress", Appl. Math. Model., 35(11), 5286-5301, https://doi.org/10.1016/j.apm.2011.04.026.
  5. Chattopadhyay, A. and Choudhury, S. (1990), "Propagation, Reflection and transmission of magneto-elastic shear waves in a self-reinforced medium", Int. J. Eng. Sci., 28, 485-495. https://doi.org/10.1016/0020-7225(90)90051-j.
  6. Chattopadhyay, A., Venkateswarlu, R.L.K. and Saha, S. (2002), "Reflection of quasi-P and quasi-SV waves at the free and rigid boundaries of a fibre-reinforced medium", Sadhana, 27(6), 613-630. https://doi.org/10.1007/bf02703354.
  7. Chaudhary, S., Kaushik, V.P. and Tomar, S.K. (2004), "Reflection and transmission of plane SH wave through a self-reinforced elastic layer between two half-spaces", Acta Geophys. Polon., 52(2), 219-235.
  8. Cowin, S.C. and Nunziato, J.W. (1979), "A nonlinear theory of elastic materials with voids", Arch. Rat. Mech. Anal., 72(2), 175-291. https://doi.org/10.1007/bf0024936.
  9. Cowin, S.C. and Nunziato, J.W. (1983), "Linear elastic materials with voids", J. Elast., 13(2), 125-147. https://doi.org/10.1007/BF00041230.
  10. Eringen, A.C. (1967), "Theory of micropolar elasticity", Int. J. Eng. Sci., 5, 191. https://doi.org/10.1016/0020-7225(67)90004-3
  11. Khan, A., Anya, A.I. and Kaneez, H. (2015), "Gravitational effects on surface waves in non-homogeneous rotating fibre- reinforced anisotropic elastic media with voids", Int. J. Appl. Sci. Eng. Res., 4(5), 620-632. https://doi.org/10.6088/ijaser.04064.
  12. Kumar, R., Gogna M.L. and Debnath L. (1990), "On lamb's plane problem in a micropolar viscoelastic half-space with stretch", Int. J. Math. Math. Sci., 13(2), 363-372. http://dx.doi.org/10.1155/S0161171290000540/
  13. Kumar, R., Sharma N. and Lata, P. (2016), "Thermomechanical interactions in transversely isotropic magnetothermoelastic medium with vacuum and with and without energy dissipation with combined effects of rotation, vacuum and two temperatures", Appl. Math. Model., 40(13-14), 2060-2075. https://doi.org/10.1016/j.apm.2016.01.061.
  14. Kumar, R., Sharma, K.D. and Garg, S.K. (2015), "Reflection of plane waves in transversely isotropic micropolar viscothermoelastic solid", Mater. Phys. Mech., 22(1), 1-14.
  15. Kumar, R., Sharma, N. and Lata, P. (2016), "Effects of Hall current in a transversely isotropic magnetothermoelastic two temperature medium with rotation and with and without energy dissipation due to normal force", Struct. Eng. Mech., 57(1), 91-103. https://doi.org/10.12989/sem.2016.57.1.091.
  16. Lata, P. (2018), "Effect of energy dissipation on plane waves in sandwiched layered thermo- elastic medium", Steel Compos. Struct., 27(2) 439-451. https://doi.org/10.12989/scs.2018.27.4.439.
  17. Lata, P. (2018), "Reflection and refraction of plane waves in layered nonlocal elastic and anisotropic thermoelastic medium", Struct. Eng. Mech., 66(1), 113-124, https://doi.org/10.12989/sem.2018.66.1.113.
  18. Masoud, N. (2018), "Seismic surface waves in a prestressedimperfectly bonded covered half-space", Geomech. Eng., 16(1), 11-19. https://doi.org/10.12989/gae.2018.16.1.011.
  19. McCarthy, M.F. and Eringen, A.C.(1969), "A problem on micropolar viscoelastic waves", Int. J. Eng. Sci., 7, 447-458. https://doi.org/10.1016/0020-7225(69)90032-9.
  20. Puri, P. and Cowin, S.C. (1985), "Plane waves in linear elastic materials with voids", J. Elast., 15(2), 167-183. https://doi.org/10.1007/bf00041991.
  21. Schoenberg, M. and Censor. D. (1973), "Elastic waves in rotating media", Quart. Appl. Math., 31(1), 115-125. https://doi.org/10.1090/qam/99708.
  22. Sengupta, P.R. and Nath, S. (2001), "Surface waves in fibrereinforced anisotropic elastic media", Sadhana, 26(4), 363-370. https://doi.org/10.1007/bf02703405.
  23. Singh, B. (2000), "Reflection and transmission of plane harmonic waves at an interface between liquid and micropolar viscoelastic solid with stretch", Sadhana, 25, 589-600. https://doi.org/10.1007/BF02703507.
  24. Singh, B. and Kumar, R. (1998), "Reflection and refraction coefficient of plane waves at an interface between micropolar elastic solid and viscoelastic solid", Int. J. Eng. Sci., 36(2), 119-135. https://doi.org/10.1016/s0020-7225(97)00041-4.
  25. Sinha, M. and Bera, R.K. (2003), "Eigenvalue approach to study the effect of rotation and relaxation time in generalized thermoelasticity", Comput. Math. Appl., 46, 783-792. https://doi.org/10.1016/s0898-1221(03)90141-6.
  26. Sunita, D., Suresh, K.S. and Kapil, K.K. (2019), "Reflection at the free surface of fibre-reinforced thermoelastic rotating medium with two temperature and phase-lag", Appl. Math. Model., 65, 106-119. https://doi.org/10.1016/j.apm.2018.08.004.
  27. Tauchert, T.R. (1971), Thermal stresses in micropolar elastic solids", Acta Mechanics, 11(3-4), 155-169. https://doi.org/10.1007/bf01176553.