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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- M. Ya. Semkiv, “Diffraction of normal SH-waves in a waveguide with a crack,” Acoustic Bulletin, vol. 14, no. 2, pp. 57–69, 2011.
- 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.
- G. Maugin, “Nonlinear waves in elastic crystals,” London: Oxford University Press, 1999.
- R. Mittra, and S. W. Lee, “Analytical Techniques in the Theory of Guided Waves,” New York: Macmillan, 1971.
- J. Miklowitz, “The theory of elastic waves and wave guides,” Amsterdam, New York, Oxford: North-Holland Publishing Company, 1978.
- 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.
- 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.
- K. F. Graff, “Wave motion in elastic solids,” New York: Dover Publications, 1991.
- R. E. Collin, “Field theory of guided waves,” New York: Wiley-IEEE Press, 1991.
- 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.
- 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.
- V. Pagneux, “Revisiting the edge resonance for Lamb waves in a semi-infinite plate,” J. Acoust. Soc. Amer., vol. 120, pp. 649– 656, 2006.
- B. Noble, “Methods based on the Wiener–Hopf technique for the solution of partial differential equations,” Belfast, Northern Ireland: Pergamon Press, 1958.
- 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.
- K.-M. Lee, “An inverse scattering problem from an impedance obstacle,” J. of Computational Physics, vol.227, pp. 431–439, 2007.
- 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.
- 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.
- 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.
- 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.
- 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.
- V. P. Shestopalov, “Spectral theory and excitation of open structures,” Кiev: Naukova Dumka, 1987.
- J. W. Brown, and R. Churchill, “Complex variables and applications,” McCraw-Hill Higher Education, Boston, 2009.