The Fourier integral transform has been used to reduce the diffraction problem of the normal SH-wave on a semi- infinite rigid inclusion in the elastic layer to the Wiener-Hopf equation. Its solution is obtained by the factorization method. The analytical expressions of the diffracted displacement fields have been represented in any region of interest. The dependences of the scattered field on the parameters of the structure have

The purpose of this paper is to model the displacement field on the layer’s surfaces with an internal defect for its further identification. For this purpose, the problem of SH-wave diffraction from the defect located in the elastic layer is solved. The defect is modelled by the rigid semi- infinite inclusion of zero thickness. Time factor is assumed to been given. The properties of identification of the inclusion type defect in the plane layer have been illustrated.

[1] Z. Nazarchuk, L. Muravsky, D. Kuryliak, “To the problem of the subsurface defects detection: theory and experiment,” Procedia Structural Integrity. vol.16, pp. 11–18, 2019, doi: 10.1016/j.prostr.2019.07.016.

[2] B. P. Thomas, P. S. Annamala, and C. S. Narayanamurthy, “Investigation of vibration excitation of debonded sandwich structures using time-average digital holography,” Applied Optics, vol. 56, pp. F7–F1, 2017.

[3] P. Fomitchov, L.-S. Wang, and S. Krishnaswamy, “Advanced image-processing techniques for automatic nondestructive evaluation of adhesively-bonded structures using speckle interferometry,” Journal of Nondestructive Evaluation, vol. 16, pp. 215–227, 1997.

[4] B. F. Pouet, S. Krishnaswamy, “Synchronized reference updating technique for electronic speckle interferometry,” Journal of Nondestructive Evaluation, vol. 12, pp. 133–138, 1993.

[5] B.F. Pouet, S. Krishnaswamy, “Additive-subtractive phase- modulated electronic speckle interferometry: analysis of fringe visibility,” Applied Optics, vol. 33, pp. 6609–6616, 1994.

[6] E. Stoykova, N. Berberova, Y. Kim, D. Nazarova, B. Ivanov, A. Gotchev, J. Hong, and H. Kang, “Dynamic speckle analysis with smoothed intensity-based activity maps,” Optica and Lasers in Engineering, vol. 93, pp. 55–65, 2017.

[7] M. V. Voytko, M. M. Kutlyk, and D. B. Kuryliak, “The resonant scattering of SH-waves by a finite crack in an elastic layer,” Journal of Taras Shevchenko University of Kyiv, Special issue, Series: of Physical and Mathematical Sciences, pp. 51–54, 2015.

[8] 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.609–623, Aug. 2013.

[9] 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.

[10] S. I. Rokhlin, “Resonance phenomena of Lamb waves scattering by a finite crack in a solid layer,” J. Acoust. Soc. Am., vol.69, no4, pp. 922–928, 1981.

[11] M. V. Voytko, Ya. P. Kulynych, and D. B. Kuryliak, “Resonant scattering of the SH-wave by the interface impedance defect in an elastic layer,” in *Proc. of 16th Int. Conf. on Mathematical Methods in Electromagnetic Theory (MMET-2016). *Lviv, Ukraine, 2016, pp. 2641267.

[12] M. Ya. Semkiv, H. M. Zrazhevskyi, and V. T. Matsypura, “Diffraction of normal SH-waves in a waveguide with a crack,” Acoustic Journal, vol. 14, no. 2, pp. 57–69, 2011.

[13] R. Mittra, S. W. Lee, “Analytical Techniques in the Theory of Guided Waves,” New York: Macmillan, 1971.

[14] B. Noble, “Methods based on the Wiener–Hopf technique for the solution of partial differential equations,” Belfast, Northern Ireland: Pergamon Press, 1958.

Myron V. Voytko was born in Svytaziv village, Sokal district, Lviv region, on June 17, 1979. He received MS degree in Physics at Ivan Franko National University of Lviv in 2001. He joined Karpenko Physico-Mechanical Institute of the National Academy of Sciences of Ukraine, Lviv, Ukraine in 2003. He served as an engineer during 2003-2007 and junior researcher during 2007-2010. Since 2010 he has been a research of the department of Physical Bases of Materials Diagnostics. He received the PhD degree in mechanics of deformable bodies at Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of the National Academy of Sciences of Ukraine, Lviv, Ukraine. His research interests are mainly in the developing of new theoretical models for the analysis of the elastic wave scattering and diffraction from various internal and interface defects of the layered materials for their diagnostics. He was honored with an award of junior scientists of the National Academy of Scientists of Ukraine in 2013. research interests are in elastic wave propagation and diffraction from the defects.

Dozyslav B. Kuryliak was born in Rava-Ruska, Lviv region, Ukraine, on November 08, 1952. He received the MS degree in radio physics and electronics at Ivan Franko State University of Lviv in 1975 (honor); received the PhD and D.Sc. degrees in radio physics in 1988 and 2002 respectively at Kharkiv State University and O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine. He joined Karpenko Physico-Mechanical Institute of the National Academy of Sciences of Ukraine, Lviv, Ukraine in 1977. He served as a senior and leading engineer in the Institute during 1977– 1991, senior researcher during 1991–2003 and leading scientist during 2003 –2007. Since 2007, he has been a Chair of the department of Physical Bases of Materials Diagnostics. His research interests are mainly in the functional-theoretical methods for rigorous analysis of wave diffraction from the canonical structures and their application for modeling of the electromagnetic, acoustic and elastic waves scattering from the defects. He is the author of two monographs and above 160 journal and conference papers. He is the winner of the Ukrainian State Prize in Science and Technology. Since 2006, he has been a professor of the Department of Electronic Computing Machines, Lviv Polytechnic National University. He has the academic ranks of Senior Researcher of Radio Science and Professor of Physics and Astronomy.

Yaroslav P. Kulynych was born in Dovhe village, Lviv region, Ukraine on February 23, 1955. He graduated from the Mathematical Department of Ivan Franko State University of Lviv, Ukraine in 1977; he worked as an engineer, junior and senior researchers at the Karpenko Physico-Mechanical Institute of the National Academy of Sciences of Ukraine, Lviv, Ukraine. In 1997 he defended his candidate-degree thesis “Mathematical modeling of signals and electromagnetic fields of marine electrical prospecting”. His research interests are in the mathematical modeling of the electromagnetic and elastic fields interaction with an inhomogeneous medium. His scientific results were obtained and developed by theoretical bases for interpretation of the eddy-current and the radio-wave non-destructive testing data for the diagnostic technologies. He is the author of one monograph and above 80 journal and conference papers. He has the academic rank of Senior Researcher of Mathematical Modeling and Computational Methods.

Mykhaylo V. Grynenko was born in Zolochiv, Lviv region, Ukraine, on October 30, 1995. He received the BS degree in mechanics in 2016 and MS degree in applied mathematics in 2018 at Ivan Franko National University of Lviv, Ukraine. Since 2018, he is the PhD student of Karpenko Physico- Mechanical Institute of the National Academy of Sciences of Ukraine, Lviv, Ukraine. His