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  3. Volume 5, Number 1, 2020
  4. SH-Wave Scattering From the Interface Defect

SH-Wave Scattering From the Interface Defect

ACPS.
2020;
Volume 5, Number 1
: pp. 45 - 50
https://doi.org/10.23939/acps2020.01.045
Authors:
  1. Myron Voytko
  2. Yaroslav Kulynych
  3. Dozyslav Kuryliak
1
Karpenko Physico-Mechanical Institute of the NAS of Ukraine
2
Karpenko Physico-Mechanical Institute of the NAS of Ukraine
3
Karpenko Physico-Mechanical Institute of the NAS of Ukraine

The problem of the elastic SH-wave diffraction from the semi-infinite interface defect in the rigid junction of the elastic layer and the half-space is solved. The defect is modeled by the impedance surface. The solution is obtained by the Wiener- Hopf method. The dependences of the scattered field on the structure parameters are presented in analytical form. Verifica¬tion of the obtained solution is presented.

Elastic layer
impedance
rigid junction
defect
diffraction
normal wave
Wiener-Hopf technique
  1. Y. S. Wang and D. Gross, “Transfer matrix method of wave propagation in a layered medium with multiple interface cracks: anti-plane case,” Journal of Applied Mechanics, vol.68, pp. 499–503, 2001.
  2. Ye.V. Glushkov, N.V. Glushkova,  and  M.V.  Golub, “Diffraction of elastic waves by an inclined crack in a layer,” J. Appl. Math. Mech., vol. 71, no. 4, pp.6431654, 2007.
  3. D. B. Kurylyak, Z. T. Nazarchuk, and M. V. Voitko, “Analysis of the field of a plane SH-wave scattered by a finite crack on the interface of materials,” Materials Science, vol. 42, no. 6, pp. 7111724, 2006.
  4. A. D. Rawlins, and Mahmood-ul-Hassan, “Wave propagation in a waveguide,” Journal of applied mathematics and mechanics: Zeitschrift für angewandte Mathematik und Mechanik, vol. 83, no. 5, pp. 3331343, 2003.
  5. F. D. Zaman, “Diffraction of SH-waves across a mixed boundary in a plate,” Mech. Res. Commun., vol. 28, no 2, pp. 171–178, 2001.
  6. S. I. Rokhlin, “Resonance phenomena  of  Lamb  waves scattering by a finite crack in a solid layer,” J. Acoust. Soc. Am., vol. 69, no. 4, pp. 9221928, 1981.
  7. Z.  T.  Nazarchuk,   D.  B.   Kuryliak,   M.   V.   Voytko,   and Ya. P. Kulynych, “On the interaction of an elastic SH-wave with an interface crack in the perfectly rigid joint of a plate with a half-space,” J. Math. Sci., vol. 192, no. 6, pp. 6091622, 2013.
  8. M. Ya. Semkiv, “Diffraction of normal SH-waves in a waveguide with a crack,” Acoustic Bulletin, vol. 14, no. 2, pp. 57–69, 2011.
  9. M. Ya. Semkiv, H. M. Zrazhevskyi, and V. T. Matsypura, “Diffraction of normal SH-waves on a finite length crack in elastic waveguide,” Acoustic Bulletin, vol. 16, no. 1, pp. 54163,  201312014.
  10. G. Maugin, “Nonlinear waves in elastic crystals,” London: Oxford University Press, 1999.
  11. R. Mittra, and S. W. Lee, “Analytical Techniques in the Theory of Guided Waves,” New York: Macmillan, 1971.
  12. J. Miklowitz, “The theory of elastic waves and wave guides,” Amsterdam, New York, Oxford: North-Holland Publishing Company, 1978.
  13. V. V. Meleshko, A. A. Bondarenko, S. A. Dovgiy, A. N. Trofimchuk, and G. J. F. van Heijst, “Elastic waveguides: history and the state of the art. I,” J. Math. Sci., vol. 162, no. 1, pp. 991120, 2009.
  14. V. V. Meleshko, A. A. Bondarenko, A. N. Trofimchuk, and R.Z. Abasov , “Elastic waveguides: history and the state of the art. II,” J. Math. Sci., vol. 1672, no. 2, pp. 1971120, 2010.
  15. K. F. Graff, “Wave motion in elastic solids,” New York: Dover Publications, 1991.
  16. R. E. Collin, “Field theory of guided waves,” New York: Wiley-IEEE Press, 1991.
  17. V. V. Mykhas’kiv, I. O. Butrak, O. M. Khay, T. I. Kilnytska and Ch. Zhang, “A frequency-domain BIEM combining DBIEs and TBIEs for 3-D crack-inclusion interaction analysis,” Comput. Methods Appl. Mech. Engrg., vol. 200, pp. 3270– 3279, 2001.
  18. E. Glushkov, N. Glushkova, M. Golub, and A. Eremin, “Resonance blocking and passing effects in two-dimensional elastic waveguides with obstacles,” J. Acoust. Soc. Am., vol. 130, pp. 113-121, 2011.
  19. V. Pagneux, “Revisiting the edge resonance for Lamb waves in a semi-infinite plate,” J. Acoust. Soc. Amer., vol. 120, pp. 649– 656, 2006.
  20. B. Noble, “Methods based on the Wiener–Hopf technique for the solution of partial differential equations,” Belfast, Northern Ireland: Pergamon Press, 1958.
  21. L. P. Castro, and D. Kapanadze, “The impedance boundary- value problem of diffraction by a strip,” J. Math. Anal. Appl., vol. 337, no. 2, pp. 103111040, 2008.
  22. K.-M. Lee, “An inverse scattering problem from an impedance obstacle,” J. of Computational Physics, vol.227, pp. 431–439, 2007.
  23. J. Cheng, J. J. Liu, and G. Nakamura, “Recovery of the shape of an obstacle and  the boundary  impedance from  the far-field pattern,” J. Math. Kyoto U., vol. 43, pp. 165-186, 2003.
  24. R. Kress, and K.-M. Lee, “Integral equation methods for scattering from an impedance crack,” J. of Computational and Appl. Math., vol. 161, no. 1, pp. 1611177, 2003.
  25. E. Glushkov, N. Glushkova, M. Golub and A. Boström, “Natural resonance frequencies, wave blocking, and energy localization  in  an  elastic  half-space  and  waveguide  with  a crack,” J. Acoust. Soc. Am., vol. 119, no. 6, pp. 3589–359, 2006.
  26. M. V. Golub, C. Zhang, and Y. Wang, “SH–wave propagation and resonance phenomena in a periodically layered composite structure with a crack,” J. Sound and Vibr., vol. 330, pp. 314113154, 2011.
  27. Yu. K. Sirenko, S. Ström, and N. P. Yashina, “Modeling and Analysis of Transient Processes in Open Resonant Structures. New Methods and Techniques,” Springer Series in Optical Sciences, Springer, Berlin, 2007.
  28. V. P. Shestopalov, “Spectral theory and excitation of open structures,” Кiev: Naukova Dumka, 1987.
  29. J. W. Brown, and R. Churchill, “Complex variables and applications,” McCraw-Hill Higher Education, Boston, 2009.