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Torsional wave in an inhomogeneous prestressed elastic layer overlying an inhomogeneous elastic half-space under the effect of rigid boundary

  • Received : 2014.10.17
  • Accepted : 2015.01.03
  • Published : 2015.10.25

Abstract

An investigation has been carried out for the propagation of torsional surface waves in an inhomogeneous prestressed layer over an inhomogeneous half space when the upper boundary plane is assumed to be rigid. The inhomogeneity in density, initial stress (tensile and compressional) and rigidity are taken as an arbitrary function of depth, where as for the elastic half space, the inhomogeneity in density and rigidity is hyperbolic function of depth. In the absence of heterogeneities of medium, the results obtained are in agreement with the same results obtained by other relevant researchers. Numerically, it is observed that the velocity of torsional wave changes remarkably with the presence of inhomogeneity parameter of the layer. Curves are compared with the corresponding curve of standard classical elastic case. The results may be useful to understand the nature of seismic wave propagation in geophysical applications.

References

  1. Achenbach JD (1973), Wave propagation in elastic solids, New York, North-Holland publishing Company.
  2. Biot, M.A. (1965), Mechanics of incremental deformation, Wiley, New York.
  3. Chattopadhyay, A., Gupta, S., Sahu, S.A. and Dhua, S. (2013), "Torsional surface waves in heterogeneous anisotropic halfspace under initial stress", Arch. Appl. Mech., 83(3), 357-366. https://doi.org/10.1007/s00419-012-0683-8
  4. Chattopadhyay, A., Gupta, S., Kumari, P. and Sharma, V.K. (2011), "Propagation of torsional wave in an inhomogeneous layer over an inhomoogeneous half-space", Mecanica, 46(4), 671-680. https://doi.org/10.1007/s11012-010-9329-5
  5. Chattaraj, R., Samal, S.K. and Debasis, S. (2015), "On torsional surface wave in dry sandy crust laid over an inhomogeneous half space", Meccanica, doi: 10.1007/s11012-015-0125-0. https://doi.org/10.1007/s11012-015-0125-0
  6. Dhua, S. and Chattopadhyay, A. (2015), "Torsional wave in an initially stressed layer lying between two inhomogeneous media", Meccanica, doi: 10.1007/s11012-015-0119-y. https://doi.org/10.1007/s11012-015-0119-y
  7. Dey, S., Gupta, A.K. and Gupta, S. (1996), "Torsional surface waves in non- homogeneous and anisotropic medium", J. Acoust. Soc. Am., 99(5), 2737-2741. https://doi.org/10.1121/1.414815
  8. Ewing, W.M., Jardetzky, W.S. and Press, F. (1957), Elastic waves in layered media, Mcgraw-Hill, New York.
  9. Gubbins, D. (1990), Seismology and plate Tectonics, Cambridge, Cambridge University Press.
  10. Gupta, S., Chattopadhyay, A., Kundu, S. and Gupta, A.K. (2010), "Effect of rigid boundary on the propagation of torsional waves in a homogeneous layer over a heterogeneous half-space", Arch. Appl. Mech., 80(2), 143-150. https://doi.org/10.1007/s00419-009-0303-4
  11. Gupta, S., Kundu, S. and Vishwakarma, S.K. (2013), "Propagation of torsional surface wave in an inhomogeneous layer over an initially stressed inhomogeneous half-space", J. Vib. Control, doi: 10.1177/1077546313493818. https://doi.org/10.1177/1077546313493818
  12. Kakar, R. and Kakar, S. (2012), "Torsional waves in prestressed fiber reinforced medium subjected to magnetic Field", J. Solid Mech., 4(4), 402-415.
  13. Kakar, R. and Gupta, K.C. (2013), "Torsional surface waves in a non-homogeneous isotropic layer over viscoelastic half-space", Interact. Multiscale Mech., 6(1), 1-14. https://doi.org/10.12989/imm.2013.6.1.001
  14. Kakar, R. and Gupta, M. (2014), "Love waves in an intermediate heterogeneous layer lying in between homogeneous and inhomogeneous isotropic elastic half-spaces", Electro. J. Geotech. Eng., 19, 7165-7185.
  15. Kakar, R. (2014), "Analysis of the effect of gravity and nonhomogeneity on Rayleigh waves in higher-order elastic-viscoelastic half-space", J. Mech. Behav. Mater., 23(3-4), 87-93.
  16. Kumari, P. and Sharma, V.K. (2014), "Propagation of torsional waves in a viscoelastic layer over an inhomogeneous half space", Acta Mechanica, 225(6), 1673-1684. https://doi.org/10.1007/s00707-013-1021-0
  17. Love, A.E.H. (1911), Some Problems of Geo-Dynamics, London, UK, Cambridge University Press.
  18. Love, A.E.H. (1944), Mathematical Theory of Elasticity, Dover Publications, Forth Edition.
  19. Vishwakarma, S.K., Gupta, S. and Verma, A.K. (2012), "Torsional wave propagation in Earth's crustal layer under the influence of imperfect interface", J. Vib. Control, doi: 10.1177/1077546312461029. https://doi.org/10.1177/1077546312461029
  20. Whittaker, E.T. and Watson, G.N. (1990), A Course in Modern Analysis; Cambridge, Cambridge University press.