Journal of Mathematical Sciences

, Volume 231, Issue 5, pp 641–649 | Cite as

Diffraction of Rayleigh Waves on a Compliant Inclusion in the Elastic Half Space

  • V. Z. Stankevich
  • I. O. Butrak
  • I. Ya. Zhbadyns’kyi

We consider a three-dimensional dynamical problem of diffraction of Rayleigh plane waves on a circular compliant inclusion in the elastic half space. To solve the problem, we use the method of boundary integral equations. The dynamical stress intensity factors in the vicinities of points of the contour of the inclusion are analyzed.


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  1. 1.
    V. A. Galazyuk and H. T. Sulym, “Stress-strain state of an unbounded medium with “cured” disk crack,” Dop. NAN Ukr., No. 10, 65–69 (2013).Google Scholar
  2. 2.
    Ye. V. Glushkov and N. V. Glushkova, “Diffraction of elastic waves by three-dimensional cracks of arbitrary shape in a plane,” Prikl. Mat. Mekh., 60, No. 2, 282–289 (1996); English translation: J. Appl. Math. Mech., 60, No 2, 277–283 (1996).Google Scholar
  3. 3.
    A. S. Grishin, “Rayleigh waves in isotropic medium. Analytic solutions and approximations,” Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 48–52 (2001); English translation: Mech. Solids, 36 (1), 38-41 (2001).Google Scholar
  4. 4.
    N. V. Zvolinskii, K. N. Shkhinek, and N. I. Chumikov, “Interaction of a plane wave with a cut in the elastic medium,” Izv. Akad. Nauk SSSR. Fiz. Zemli, No. 4, 36–46 (1983).Google Scholar
  5. 5.
    G. S. Kit and M. V. Khai, Method of Potentials in Three-Dimensional Problems of Thermoelasticity for Bodies with Cracks [in Russian], Naukova Dumka, Kiev (1989).Google Scholar
  6. 6.
    H. S. Kit and V. Z. Stankevych, “Diffraction of Rayleigh waves on a surface crack in the half space,” Mat. Met. Fiz.-Mekh. Polya, 45, No. 3, 118–123 (2002).zbMATHGoogle Scholar
  7. 7.
    V. V. Mykhas’kiv, I. O. Butrak, and I. P. Laushnik, “Interaction between a compliant disk-shaped inclusion and a crack upon incidence of an elastic wave,” Prikl. Mekh. Tekh. Fiz., 54, No. 3, 141–148 (2013); English translation: J. Appl. Mech. Tech. Phys., 54, No. 3, 465–471 (2013).Google Scholar
  8. 8.
    V. G. Popov, “Interaction of a plane harmonic Rayleigh wave with a thin rigid edge inclusion coupled with an elastic medium,” Prikl. Mat. Mekh., 61, No. 2, 255–262 (1997); English translation: J. Appl. Math. Mech., 61, No. 2, 245–252 (1997).Google Scholar
  9. 9.
    V. G. Popov and A. É. Ulanovskii, “Comparative analysis of diffraction fields in the case of elastic waves passing through defects of different nature,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 4, 99–109 (1995).Google Scholar
  10. 10.
    V. Z. Stankevich and M. V. Khai, “Study into the interaction of cracks in an elastic half space under a shock load by means of boundary integral equations,” Prikl. Mekh., 38, No. 4, 69–76 (2002); English translation: Int. Appl. Mech., 38, No. 4, 440–446 (2002).Google Scholar
  11. 11.
    A. Boström, T. Grahn, and A. J. Niklasson, “Scattering of elastic waves by a rectangular crack in an anisotropic half space,” Wave Motion, 38, No. 2, 91–107 (2003).CrossRefzbMATHGoogle Scholar
  12. 12.
    I. Castro and A. Tadeu, “Coupling of the BEM with the MFS for the numerical simulation of frequency domain 2-D elastic wave propagation in the presence of elastic inclusions and cracks,” Eng. Anal. Bound. Elem., 36, No. 2, 169–180 (2012).MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    S. Kanaun, “Scattering of monochromatic elastic waves on a planar crack of arbitrary shape,” Wave Motion, 51, No. 2, 360–381 (2014).MathSciNetCrossRefGoogle Scholar
  14. 14.
    V. V. Matus and Ya. I. Kunets, “Null field method of SH-wave scattering by partially debonded elastic inclusion,” in: DIPED–2008. Proc. of the 13th Internat. Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory, Lviv–Tbilisi (2008), pp. 176–178.Google Scholar
  15. 15.
    V. Mykhas’kiv, “Transient response of a plane rigid inclusion to an incident wave in an elastic solid,” Wave Motion, 41, No. 2, 133–144 (2005).MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    V. V. Panasyuk, V. I. Marukha, and V. P. Sylovanyuk, Injection Technologies for the Repair of Damaged Concrete Structures, Springer, Dordrecht (2014).CrossRefGoogle Scholar
  17. 17.
    J. Pujol, Elastic Wave Propagation and Generation in Seismology, Cambridge Univ. Press, Cambridge (2003).CrossRefGoogle Scholar
  18. 18.
    V. Skalsky, O. Stankevych, and O. Serhiyenko, “Wave displacement field at a half space surface caused by an internal crack under twisting load,” Wave Motion, 50, No. 2, 326–333 (2013).MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • V. Z. Stankevich
    • 1
  • I. O. Butrak
    • 1
  • I. Ya. Zhbadyns’kyi
    • 1
  1. 1.Pidstryhach Institute for Applied Problems in Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

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