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Diffraction of Love waves by a stress-free crack of finite width in the plane interface of a layered composite

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Abstract

A rigorous theory of the diffraction of Love waves by a stress-free crack of finite width in the interface of a layered composite is presented. The incident wave is taken to be either a bulk wave or a Love-wave mode. The resulting boundary-value problem for the unknown jump in the particle displacement across the crack is solved by employing the integral equation method. The unknown quantity is expanded in terms of a complete sequence of expansion functions in which each separate term satisfies the edge condition. This leads to an infinite system of linear, algebraic equations for the coefficients of the expansion functions. This system is solved numerically. The scattering matrix of the crack, which relates the amplitudes of the outgoing waves to the amplitudes of the incident waves, is computed. Several reciprocity and power-flow relations are obtained. Numerical results are presented for a range of material constants and geometrical parameters.

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References

  1. Aki K, KL Larner, “Surface motion of a layered medium having an irregular interface due to incident plane SH waves”, Journ Geophys Res 75, (1970) pp 933–954.

    Google Scholar 

  2. Boore DM, “Love waves in nonuniform waveguides: finite difference calculations”, Journ Geophys Res 75, (1970) pp 1512–1527.

    Google Scholar 

  3. Lysmer J, LA Drake, “The propagation of Love waves across nonhorizontally layered structures”, Bull Seism Soc Am 61, (1971) pp 1233–1251.

    Google Scholar 

  4. Gregersen S, LE Alsop, “Amplitudes of horizontally refracted Love waves”, Bull Seism Soc Am 64, (1974) pp 535–553.

    Google Scholar 

  5. Hang-Sheng Tuan, Chi-Pin Chang, “Tapping of Love waves in an isotropic surface waveguide by surface-to-bulk wave transduction”, IEEE Trans Microwave Theory Techn MTT-20, (1972) pp 472–477.

    Google Scholar 

  6. Quak D, FL Neerhoff, “Reflection, transmission and excitation of SH-surface waves by a discontinuity in mass-loading on a semi-infinite elastic medium”, Appl Sci Res 29, (1974) pp 447–460.

    Google Scholar 

  7. Neerhoff FL, “Scattering of SH-waves by an irregularity at the mass-loaded boundary of a semi-infinite elastic medium”, Proc R Soc Lond A 342, (1975) pp 237–257.

    Google Scholar 

  8. Neerhoff FL, “Scattering and excitation of SH-surface waves by a protrusion at the mass-loaded boundary of an elastic half-space”, Appl Sci Res 32, (1976) pp 269–282.

    Google Scholar 

  9. Ghosh ML, “On the propagation of Love waves in an elastic layer in the presence of a vertical crack”, Proc Vibr Probl 15, (1974) pp 147–165.

    Google Scholar 

  10. Keer LM, WC Luong, “Diffraction of waves and stress intensity factors in a cracked layered composite”, J Acoust Soc Am 56, (1974) pp 1681–1686.

    Google Scholar 

  11. Kazi MH, “Diffraction of Love waves by perfectly rigid and perfectly weak half-planes”, Bull Seism Soc Am 65, (1975) pp 1461–1479.

    Google Scholar 

  12. Kraut EA, “Review of theories of scattering of elastic waves by cracks”, IEEE Trans Son Ultrason SU-23, (1976) pp 162–167.

    Google Scholar 

  13. Ewing M, WS Jardetzky and F Press, Elastic Waves in Layered Media. New-York, McGraw-Hill, (1957) pp 205–210.

    Google Scholar 

  14. Karl FC, SN Karp, “Stress behaviour in the neighbourhood of sharp corners”, Geophysics XXIX, (1964) pp 360–369.

    Google Scholar 

  15. Rayleigh Lord, “Some general theorems relating to vibrations”, London Math Soc Proc 4, (1873) pp 357–368.

    Google Scholar 

  16. Abramowitz M, IA Stegun, Handbook of Mathematical Functions, New-York, Dover Publications, (1970) p 360.

    Google Scholar 

  17. Felsen LB, N Marcuvitz, Radiation and Scattering of Waves, Englewood Cliffs, Prentice-Hall Inc (1973) pp 462 and 370.

    Google Scholar 

  18. Abramowitz M, IA Stegun, loc cit p

    Google Scholar 

  19. Abramowitz M, IA Stegun, loc cit p

    Google Scholar 

  20. Abramowitz M, IA Stegun, loc cit p

    Google Scholar 

  21. Abramowitz M, IA Stegun, loc cit p

    Google Scholar 

  22. Abramowitz M, IA Stegun, loc cit p

    Google Scholar 

  23. Bullen KE, The Earth's Density, London, Chapman and Hall (1975) p 165.

    Google Scholar 

  24. Bullen KE, loc cit pp 254 and 275

    Google Scholar 

  25. Tan TH, “Diffraction theory for time-harmonic elastic waves”, Ph.D. Thesis, Delft University of Technology, Delft, the Netherlands, (1975) p 89.

    Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, Laboratory of Electromagnetic Research, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands

    Fred L. Neerhoff

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  1. Fred L. Neerhoff
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Neerhoff, F.L. Diffraction of Love waves by a stress-free crack of finite width in the plane interface of a layered composite. Appl. Sci. Res. 35, 265–315 (1979). https://doi.org/10.1007/BF00418217

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  • DOI: https://doi.org/10.1007/BF00418217

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