DOI QR코드

DOI QR Code

Dispersion of shear wave in a pre-stressed hetrogeneous orthotropic layer over a pre-stressed anisotropic porous half-space with self-weight

  • Received : 2016.02.03
  • Accepted : 2016.04.04
  • Published : 2016.09.25

Abstract

The purpose of this study is to illustrate the propagation of the shear waves (SH-waves) in a prestressed hetrogeneous orthotropic media overlying a pre-stressed anisotropic porous half-space with self weight. It is considered that the compressive initial stress, mass density and moduli of rigidity of the upper layer are space dependent. The proposed model is solved to obtain the different dispersion relations for the SH-wave in the elastic-porous medium of different properties. The effects of compressive and tensile stresses along with the heterogeneity, porosity, Biot's gravity parameter on the dispersion of SH-wave are shown numerically. The wave analysis further indicates that the technical parameters of upper and lower half-space affect the wave velocity significantly. The results may be useful to understand the nature of seismic wave propagation in geophysical applications and in the field of earthquake and material science engineering.

Keywords

References

  1. Abd-Alla, A.M., Nofal, T.A., Abo-Dahab, S.M. and Al-Mullise, A, (2013), "Surface waves propagation in fibre reinforced anisotropic elastic media subjected to gravity field", Int. J. Phys. Sci, 8, 574-584. https://doi.org/10.5897/IJPS2013.3812
  2. Biot, M.A. (1965), Mechanics of incremental deformations, John Wiley & Sons, New York.
  3. Chattaraj, R. and Samal, S.K. (2013), "Love waves in the fibrereinforced layer over a gravitating porous half-space", Acta Geophysica, 61, 1170-1183. https://doi.org/10.2478/s11600-012-0100-2
  4. Chattaraj, R., Samal, S.K. and Mahanti, N.C. (2013), "Dispersion of Love wave propagating in irregular anisotropic porous stratum under initial stress", Int. J. Geomech., 13, 402-408. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000230
  5. Chattopadhyay, A. and De, R.K. (1983), "Love type waves in a porous layer with irregular interface", Int. J. Eng. Sci., 21, 1295-1303. https://doi.org/10.1016/0020-7225(83)90126-X
  6. Chattopadhyay, A., Gupta, S., Kumari, P. and Sharma, V.K. (2012), "Effect of point source and heterogeneity on the propagation of SH-waves in a viscoelastic layer over a viscoelastic half-space", Acta Geophysica, 60(1), 119-139. https://doi.org/10.2478/s11600-011-0059-4
  7. Chattopadhyay, A., Gupta, S., Sharma, V.K. and Kumari, P. (2010), "Effect of point source and heterogeneity on the propagation of SH-waves", Int. J. Appl. Math. Mech., 6(9), 76-89.
  8. Chattopadhyay, A., Singh, A.K. and Dhua, S. (2014), "Effect of heterogeneity and reinforcement on propagation of a crack due to shear waves", Int. J. Geomech., 14(4), 04014013. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000356
  9. Dey, S. and Gupta, S. (1987), "Longitudinal and shear waves in an elastic medium with void pores", Proceedings of the IndianNational Science Academy, 53, 554-563
  10. Ewing, W.M., Jardetzky, W.S. and Press, F. (1957), Elastic waves in layered media, New York, McGraw-Hill.
  11. Ghorai, A.P., Samal, S.K. and Mahanty, 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, 1873-1883. https://doi.org/10.1016/j.apm.2009.10.004
  12. Gupta, R.R. and Gupta, R.R. (2013), "Analysis of wave motion in an anisotropic initially stressed fiber reinforced thermoelastic medium", Earthq. Struct., 4(1), 1-10. https://doi.org/10.12989/eas.2013.4.1.001
  13. Gupta, S., Vishwakarma, S.K., Majhi, D.K. and Kundu, S. (2013), "Possibility of Love wave propagation in a porous layer under the effect of linearly varying directional rigidities", Appl. Math. Model., 37, 6652-6660. https://doi.org/10.1016/j.apm.2013.01.008
  14. Kundu, S., Manna, S. and Gupta, S. (2014), "Propagation of SH-wave in an initially stressed orthotropic medium sandwiched by a homogeneous and a heterogeneous semi-infinite media", Math. Meth. Appl. Sci., 38(9), 1926-1936. https://doi.org/10.1002/mma.3203
  15. Love, A.E.H. (1911), Some Problems of Geo-Dynamics, Cambridge University Press, London, UK.
  16. Sahu, S.A., Saroj, P.K. and Paswan, B. (2014), "Shear waves in a heterogeneous fiber-reinforced layer over a half-space under gravity", Int. J. Geomech., 15(2), 04014048.
  17. Watanabe, K. and Payton, R.G. (2002), "Green's function for SH waves in a cylindrically monoclinic material", J. Mech. Phys. Solid., 50, 2425-2439. https://doi.org/10.1016/S0022-5096(02)00026-1
  18. Whitham, G.B. (1974), Linear and nonlinear waves, Wiley.
  19. Whittaker, E.T. and Watson, G.N. (1991), A course of modern analysis, Universal Book Stall, New Delhi, India.

Cited by

  1. Scattering of torsional surface waves in a three layered model structure vol.68, pp.4, 2018, https://doi.org/10.12989/sem.2018.68.4.443
  2. Comparative study of torsional wave profiles through stratified media with fluted boundaries vol.74, pp.1, 2016, https://doi.org/10.12989/sem.2020.74.1.091
  3. Evolution characteristics of mining fissures in overlying strata of stope after converting from open-pit to underground vol.14, pp.24, 2016, https://doi.org/10.1007/s12517-021-08978-0