Geomechanics and Engineering

  • 제10권2호
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  • Pages.137-154
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  • 2016
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  • 2005-307X(pISSN)
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  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
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Rayleigh wave in an anisotropic heterogeneous crustal layer lying over a gravitational sandy substratum

  • 투고 : 2015.05.03
  • 심사 : 2015.12.31
  • 발행 : 2016.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

The purpose of this paper is to study the propagation of Rayleigh waves in an anisotropic heterogeneous crustal layer over a gravitational semi-infinite sandy substratum. It is assumed that the heterogeneity in the crustal layer arises due to exponential variation in elastic coefficients and density whereas the semi-infinite sandy substratum has homogeneous sandiness parameters. The coupled effects of heterogeneity, anisotropy, sandiness parameters and gravity on Rayleigh waves are discussed analytically as well as numerically. The dispersion relation is obtained in determinant form. The proposed model is solved to obtain the different dispersion relations for the Rayleigh wave in the elastic medium of different properties. The results presented in this study may be attractive and useful for mathematicians, seismologists and geologists.

키워드

참고문헌

  1. Abd-Alla, A.M. and Ahmed, S.M. (1997), "Rayleigh waves in an orthotropic thermoelastic medium under gravity field and initial stress", Earth Moon Planets, 75(3), 185-197. https://doi.org/10.1007/BF02592996
  2. Abd-Alla, A.M., Mahmoud, S.R., Abo-Dahab, S.M. and Helmy, M.I. (2010), "Influences of rotation, magnetic field, initial stress, and gravity on Rayleigh waves in a homogeneous orthotropic elastic halfspace", Appl. Math. Sci., 4(2), 91-108.
  3. Abd-Alla, A.M., Abo-Dahab, S.M. and Bayones, F.S. (2011), "Rayleigh waves in generalized magnetothermo-viscoelastic granular medium under the influence of rotation, gravity field, and initial stress", Math. Prob. Eng., 1-47.
  4. Acharya, D.P. and Monda, A. (2002), "Propagation of Rayleigh surface waves with small wavelengths in nonlocal visco-elastic solids", Sadhana, 27(6), 605-612. https://doi.org/10.1007/BF02703353
  5. Addy, S.K. and Chakraborty, N. (2005), "Rayleigh waves in a viscoelastic half-space under initial hydrostatic stress in presence of the temperature field", Int. J. Math. Math. Sci., 24, 3883-3894.
  6. Biot, M.A. (1965), Mechanics of Incremental Deformations, John Wiley & Sons, New York, NY, USA.
  7. Bromwich, T.J. (1898), "On the influence of gravity on elastic waves, and, in particular, on the vibrations of an elastic globe", Proc. London Math. Soc., 30(1), 98-120.
  8. Favretto-Cristini, N., Komatitsch, D., Carcione, J.M. and Cavallini, F. (2011), "Elastic surface waves in crystals. Part 1: Review of the physics", Ultrasonics, 51(6), 653-660. https://doi.org/10.1016/j.ultras.2011.02.007
  9. Ghatuary, R. and Chakraborty, N. (2015), "Thermomagnetic effect on the propagation of Rayleigh waves in an isotropic homogeneous elastic half-space under initial stress", Cogent Engineering, 2(1), 1026539. https://doi.org/10.1080/23311916.2015.1026539
  10. Gupta, I.S. (2013), "Propagation of Rayleigh waves in a prestressed layer over a prestressed half-space", Frontiers in Geotechnical Engineering (FGE), 2(1), 16-22.
  11. Kumar, R. and Singh, J. (2011), "Propagation of Rayleigh waves through the surface of an elastic solid medium in the presence of a mountain", Int. J. Appl. Sci. Technol., 1(4), 50-58.
  12. Love, A.E.H. (1911), Some Problems of Geodynamics, Cambridge University Press, Cambridge, UK.
  13. Pal, P.C., Kumar, S. and Bose, S. (2014), "Propagation of Rayleigh waves in anisotropic layer overlying a semi-infinite sandy medium", Ain Shams Eng. J., 6(2), 621-627. DOI: 10.1016/j.asej.2014.11.003
  14. Sethi, M., Gupta, K.C., Sharma, R. and Malik, D. (2012), "Propagation of Rayleigh waves in nonhomogeneous elastic half-space of orthotropic material under initial compression and influence of gravity", Math. Aeterna, 2(10), 901-910.
  15. Singh, B. and Bala, K. (2013), "On Rayleigh wave in two-temperature generalized thermoelastic medium without energy dissipation", Appl. Math., 4(1), 107-112.
  16. Vashishth, A.K. and Sharma, M.D. (2008), "Propagation of plane waves in poroviscoelastic anisotropic media", Appl. Math. Mech., 29(9), 1141-1153. https://doi.org/10.1007/s10483-008-0904-x
  17. Vinh, P.C. (2009), "Explicit secular equations of Rayleigh waves in elastic media under the influence of gravity and initial stress", Appl. Math. Comput., 215(1), 395-404. https://doi.org/10.1016/j.amc.2009.05.014
  18. Vinh, P.C. and Seriani, G. (2009), "Explicit secular equations of Rayleigh waves in a non-homogeneous orthotropic elastic medium under the influence of gravity", Wave Motion, 46(7), 427-434. https://doi.org/10.1016/j.wavemoti.2009.04.003
  19. Vishwakarma, S.K. and Gupta, S. (2014), "Rayleigh wave propagation: A case wise study in a layer over a half space under the effect of rigid boundary", Arch. Civil Mech. Eng., 14(1), 181-189. https://doi.org/10.1016/j.acme.2013.07.007
  20. Weiskopf, W.H. (1945), "Stresses in soils under a foundation", J. Frank. Inst., 239(6), 445-453. https://doi.org/10.1016/0016-0032(45)90189-X
  21. Wilson, J.T. (1942), "Surface waves in a heterogeneous medium", Bull. Seismol. Soc. Am., 32(4), 297-305.

피인용 문헌

  1. On the elastic parameters of the strained media vol.67, pp.1, 2016, https://doi.org/10.12989/sem.2018.67.1.053
  2. Shear wave propagation in a slightly compressible finitely deformed layer over a foundation with pre-stressed fibre-reinforced stratum and dry sandy viscoelastic substrate vol.31, pp.5, 2016, https://doi.org/10.1080/17455030.2019.1631503
  3. Frequency shifts and thermoelastic damping in different types of Nano-/Micro-scale beams with sandiness and voids under three thermoelasticity theories vol.510, pp.None, 2021, https://doi.org/10.1016/j.jsv.2021.116301