Earthquakes and Structures

  • 제12권6호
  • /
  • Pages.619-628
  • /
  • 2017
  • /
  • 2092-7614(pISSN)
  • /
  • 2092-7622(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

On Propagation of Love waves in dry sandy medium sandwiched between fiber-reinforced layer and prestressed porous half-space

  • Gupta, Shishir (Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines)) ;
  • Ahmed, Mostaid (Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines))
  • 투고 : 2016.02.16
  • 심사 : 2017.05.26
  • 발행 : 2017.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

The intent of this paper is to investigate the propagation of Love waves in a dry sandy medium sandwiched between fiber-reinforced layer and prestressed porous half-space. Separate displacement components have been deduced in order to characterize the dynamics of individual materials. Using suitable boundary conditions, the frequency equation has been derived by means of separation of variables which reveals the significant role of reinforcement parameters, sandiness, thickness of layers, porosity and prestress on the wave propagation. The phase velocity of the Love wave has been discussed in accordance with its typical cases. In both cases when fiber-reinforced and dry sandy media are absent, the derived equation of Love type wave coincides with the classical Love wave equation. Numerical computations have been performed in order to graphically illustrate the dependencies of different parameters on phase velocity of Love waves. It is observed that the phase velocity decreases with the increase of parameters pertaining to reinforcement and prestress. The results have certain potential applications in earthquake seismology and civil engineering.

키워드

과제정보

연구 과제 주관 기관 : University Grants Commission, New Delhi

참고문헌

  1. Achenbach, J.D. (1973), Wave propagation in elastic solids, North-Holland Pub. Company, Amsterdam.
  2. Belfield, A.J., Rogers, T.G. and Spencer, A.J.M. (1983), "Stress in elastic plates reinforced by fibres lying in concentric circles", J. Mech. Phys. Solids, 31(1), 25-54. https://doi.org/10.1016/0022-5096(83)90018-2
  3. Biot, M.A. (1965), Mechanics of Incremental Deformations, Wiley, New York.
  4. Boxberg, M.S., Prevost, J.H. and Tromp, J. (2015), "Wave propagation in porous media saturated with two fluids", Trans. Porous Media, 107(1), 49-63. https://doi.org/10.1007/s11242-014-0424-2
  5. Bullen, K.E. (1963), An Introduction to the Theory of Seismology, Cambridge University Press, Cambridge.
  6. Chattaraj, R. and Samal, S.K. (2013), "Love waves in the fiberreinforced layer over a gravitating porous half-space", Acta Geophysica, 61(5), 1170-1183. https://doi.org/10.2478/s11600-012-0100-2
  7. Chattopadhyay, A. and Singh, A.K. (2012), "Propagation of magnetoelastic shear waves in an irregular self-reinforced layer", J. Eng. Math., 75(1), 139-155. https://doi.org/10.1007/s10665-011-9519-8
  8. Chaudhary, S., Kaushik, V.P. and Tomar, S.K. (2005), "Transmission of shear waves through a self-reinforced layer sandwiched between two inhomogeneous viscoelastic halfspaces", Int. J. Mech. Sci., 47(9), 1455-1472. https://doi.org/10.1016/j.ijmecsci.2005.04.011
  9. Chen W.Y., Xia, T.D., Sun, M.M. and Zhai, C.J. (2012), "Transverse wave at a plane interface between isotropic elastic and unsaturated porous elastic solid half-spaces", Transport in Porous Media, 94(1), 417-436. https://doi.org/10.1007/s11242-012-0012-2
  10. Ghorai, A.P., Samal, S.K. and Mahanti, N.C. (2010), "Love waves in a fluid-saturated porous layer under a rigid boundary and lying over an elastic half-space under gravity", Appl. Math. Model., 34(5), 1873-1883. https://doi.org/10.1016/j.apm.2009.10.004
  11. Kakar, R. (2015), "SH-wave propagation in a heterogeneous layer over an inhomogeneous isotropic elastic half-space", Earthq. Struct., 9(2), 305-320. https://doi.org/10.12989/eas.2015.9.2.305
  12. Kakar, R. and Kakar, S. (2015), "Torsional wave in an inhomogeneous prestressed elastic layer overlying an inhomogeneous elastic half-space under the effect of rigid boundary", Earthq. Struct., 9(4), 753-766. https://doi.org/10.12989/eas.2015.9.4.753
  13. Kakar, R. (2016), "Modeling of SH-waves in a fiber-reinforced anisotropic layer", Earthq. Struct., 10(1), 91-104. https://doi.org/10.12989/eas.2016.10.1.091
  14. Gubbins, D. (1990), Seismology and Plate Tectonics, Cambridge University Press, London.
  15. Ke, L.L., Wang, J.S. and Zhang, Z.M. (2006), "Love waves in an inhomogeneous fluid saturated porous layered half-space with linearly varying properties", Soil Dyn. Earthq. Eng., 26(6), 574-581. https://doi.org/10.1016/j.soildyn.2006.01.010
  16. Khurana, P. and Vashisth, A.K. (2001), "Love wave propagation in a pre-stressed medium", Indian J. Pure Appl. Math., 32(8), 1201-1207.
  17. Kielczyn'ski, P., Szalewski, M. and Balcerzak, A. (2012), "Effect of a viscous liquid loading on Love wave propagation", Int. J. Solid. Struct., 49(17), 2314-2319. https://doi.org/10.1016/j.ijsolstr.2012.04.030
  18. Kundu, S., Gupta, S. and Manna, S. (2014a), "Propagation of Love wave in fiber-reinforced medium lying over an initially stressed orthotropic half-space", Int. J. Numer. Anal. Method. Geomech., 38(11), 1172-1182. https://doi.org/10.1002/nag.2254
  19. Kundu, S., Gupta, S., Manna, S. and Dolai, P. (2014b), "Propagation of Love wave in fiber-reinforced medium over a nonhomogeneous half-space", Int. J. Appl. Mech., 6(5), 1450050. https://doi.org/10.1142/S1758825114500501
  20. Love, A.E.H. (1927), Mathematical Theory of Elasticity, Dover, New York.
  21. Pal, J. and Ghorai, A.P. (2015), "Propagation of Love wave in sandy layer under initial stress above anisotropic porous halfspace under gravity", Trans. Porous Media, 109(2), 297-316. https://doi.org/10.1007/s11242-015-0519-4
  22. Pradhan, A., Samal, S.K. and Mahanti, N.C. (2003), "Influence of anisotropy on the Love waves in a self-reinforced medium", Tamkang J. Sci. Eng., 6(3), 173-178.
  23. Sengupta, P.R. and Nath, S. (2001), "Surface waves in an anisotropic elastic medium", Sadhana, 26(4), 363-370. https://doi.org/10.1007/BF02703405
  24. Singh, B. and Singh, S.J. (2004), "Reflection of plane waves at the free surface of a fiber-reinforced elastic half-space", Sadhana, 29(3), 249-257. https://doi.org/10.1007/BF02703774
  25. Son, M.S. and Kang, Y.J. (2012), "Propagation of shear waves in a poroelastic layer constrained between two elastic layers", Appl. Math. Model., 36(8), 3685-3695. https://doi.org/10.1016/j.apm.2011.11.008
  26. Spencer, A.J.M. (1972), Deformations of Fiber-Reinforced Materials, Oxford University Press, London.
  27. Tomar, S.K. and Kaur, J. (2007), "SH-waves at a corrugated interface between a dry sandy half-space and an anisotropic elastic half-space", Acta Mechanica, 190(1), 1-28. https://doi.org/10.1007/s00707-006-0423-7
  28. Tomar, S.K. and Singh, S.S. (2006), "Plane SH-waves at a corrugated interface between two dissimilar perfectly conducting self-reinforced elastic half-spaces", Int. J. Numer. Anal. Method. Geomech., 30(6), 455-487. https://doi.org/10.1002/nag.485