Advertisement

Influence of prestress and periodic corrugated boundary surfaces on Rayleigh waves in an orthotropic medium over a transversely isotropic dissipative semi-infinite substrate

Regular Article

Abstract.

The paper environs the study of Rayleigh-type surface waves in an orthotropic crustal layer over a transversely isotropic dissipative semi-infinite medium under the effect of prestress and corrugated boundary surfaces. Separate displacement components for both media have been derived in order to characterize the dynamics of individual materials. Suitable boundary conditions have been employed upon the surface wave solutions of the elasto-dynamical equations that are taken into consideration in the light of corrugated boundary surfaces. From the real part of the sixth-order complex determinantal expression, we obtain the frequency equation for Rayleigh waves concerning the proposed earth model. Possible special cases have been envisaged and they fairly comply with the corresponding results for classical cases. Numerical computations have been performed in order to graphically demonstrate the role of the thickness of layer, prestress, corrugation parameters and dissipation on Rayleigh wave velocity. The study may be regarded as important due to its possible applications in delay line services and investigating deformation characteristics of solids as well as typical rock formations.

References

  1. 1.
    L. Rayleigh, Proc. London Math. Soc. 17, 4 (1885)MathSciNetCrossRefGoogle Scholar
  2. 2.
    T.J. Bromwich, Proc. London Math. Soc. 30, 98 (1898)CrossRefGoogle Scholar
  3. 3.
    A.M. Abd-Alla, Appl. Math. Comput. 99, 61 (1999)MathSciNetGoogle Scholar
  4. 4.
    A.M. Abd-Alla, S.M. Abo-Dahab, H.A.H. Hammad, Appl. Math. Model. 35, 2981 (2011)MathSciNetCrossRefGoogle Scholar
  5. 5.
    K. Liu, Y. Liu, J. Sound Vib. 271, 1 (2004)ADSCrossRefGoogle Scholar
  6. 6.
    P.C. Vinh, V.T.N. Anh, N.T.K. Linh, Waves Random Complex Media 26, 176 (2016)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    P.C. Vinh, V.T.N. Anh, Meccanica (2016) DOI:10.1007/s11012-016-0464-5
  8. 8.
    P.C. Vinh, R.W. Ogden, Meccanica 40, 147 (2005)MathSciNetCrossRefGoogle Scholar
  9. 9.
    S.K. Vishwakarma, S. Gupta, Arch. Civil Mech. Eng. 14, 181 (2014)CrossRefGoogle Scholar
  10. 10.
    S. Kostić, N. Vasović, M. Perc, M. Toljić, D. Nikolić, Physica A 392, 4134 (2013)ADSCrossRefGoogle Scholar
  11. 11.
    S. Kostić, I. Franović, M. Perc, N. Vasović, K. Todorović, Sci. Rep. 4, 5401 (2014)ADSGoogle Scholar
  12. 12.
    V.T. Buchwald, Q. J. Mech. Appl. Math. XIV, 293 (1961)CrossRefGoogle Scholar
  13. 13.
    B. Singh, J. Solid Mech. 5, 270 (2013)Google Scholar
  14. 14.
    B. Singh, Arc. Appl. Mech. 77, 253 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    J.N. Sharma, M. Pal, D. Chand, J. Sound Vib. 284, 227 (2005)ADSCrossRefGoogle Scholar
  16. 16.
    A. Bucur, Acta Mech. 227, 1199 (2016)MathSciNetCrossRefGoogle Scholar
  17. 17.
    S. Chiriţă, J. Elasticity 110, 185 (2013)CrossRefGoogle Scholar
  18. 18.
    B. Singh, R. Sindhu, J. Singh, Eng. Solid Mech. 4, 11 (2016)CrossRefGoogle Scholar
  19. 19.
    S. Shekhar, I.A. Parvez, Appl. Math. 4, 107 (2013)CrossRefGoogle Scholar
  20. 20.
    P.V. Krauzin, D.S. Goldobin, Eur. Phys. J. Plus 129, 221 (2014)CrossRefGoogle Scholar
  21. 21.
    K. Tanuma, C.S. Man, Y. Chen, Int. J. Eng. Sci. 92, 63 (2015)CrossRefGoogle Scholar
  22. 22.
    E.V. Glushkov, N.V. Glushkova, S.I. Fomenko, Acoust. Phys. 57, 230 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    M.A. Hayes, R.S. Rivlin, Arch. Ration. Mech. Anal. 8, 358 (1961)CrossRefGoogle Scholar
  24. 24.
    M. Destrade, N.H. Scott, Wave Motion 40, 347 (2004)MathSciNetCrossRefGoogle Scholar
  25. 25.
    M. Destrade, M. Ottenio, A.V. Pichugin, G.A. Rogerson, Int. J. Eng. Sci. 43, 1092 (2005)CrossRefGoogle Scholar
  26. 26.
    R.T. Edmondson, Y.B. Fu, Int. J. Non-Linear Mech. 44, 530 (2009)ADSCrossRefGoogle Scholar
  27. 27.
    P.C. Vinh, N.T.K. Linh, Meccanica 48, 2051 (2013)MathSciNetCrossRefGoogle Scholar
  28. 28.
    S. Kostić, M. Perc, N. Vasović, S. Trajković, PLoS ONE 8, e82056 (2013)ADSCrossRefGoogle Scholar
  29. 29.
    J.T. Kuo, J.E. Nape, Bull. Seismol. Soc. Am. 52, 807 (1962)Google Scholar
  30. 30.
    S.S. Singh, J. Vib. Control 17, 789 (2010)CrossRefGoogle Scholar
  31. 31.
    S.K. Vishwakarma, R. Xu, Appl. Math. Model. 40, 8647 (2016)MathSciNetCrossRefGoogle Scholar
  32. 32.
    T. Kaur, S.K. Sharma, A.K. Singh, Meccanica 51, 2449 (2016)MathSciNetCrossRefGoogle Scholar
  33. 33.
    P. Kumari, C. Modi, V.K. Sharma, Eur. Phys. J. Plus 131, 263 (2016)CrossRefGoogle Scholar
  34. 34.
    L. Li, P.J. Wei, X. Guo, Appl. Math. Model. 40, 8326 (2016)MathSciNetCrossRefGoogle Scholar
  35. 35.
    S. Asano, Bull. Seismol. Soc. Am. 56, 201 (1966)Google Scholar
  36. 36.
    M.A. Biot, Mechanics of Incremental Deformations (Wiley, New York, 1965)Google Scholar
  37. 37.
    Y.C. Fung, Foundation of Solid Mechanics (Prentice Hall of India, New Delhi, 1965)Google Scholar
  38. 38.
    D. Gubbins, Seismology and Plate Tectonics (Cambridge University Press, Cambridge, 1990)Google Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)JharkhandIndia

Personalised recommendations