Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2017-1pp.35-40

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212

<< Previous article | Volume 52, Issue 1 / 2017 | Next article >>
M.Sh. Israilov and S.E. Nosov, "Generalization of the Kirchhoff Theory to Elastic Wave Diffraction Problems," Mech. Solids. 52 (1), 35-40 (2017)
Year 2017 Volume 52 Number 1 Pages 35-40
DOI 10.3103/S0025654417010058
Title Generalization of the Kirchhoff Theory to Elastic Wave Diffraction Problems
Author(s) M.Sh. Israilov (Research Institute of Mathematical Physics and Seismodynamics, Chechen State University, ul. Kievskaya 33, Groznyy, 364037 Russia, israiler@hotmail.com)
S.E. Nosov (Research Institute of Mathematical Physics and Seismodynamics, Chechen State University, ul. Kievskaya 33, Groznyy, 364037 Russia)
Abstract The Kirchhoff approximation in the theory of diffraction of acoustic and electromagnetic waves by plane screens assumes that the field and its normal derivative on the part of the plane outside the screen coincides with the incident wave field and its normal derivative, respectively. This assumption reduces the problem of wave diffraction by a plane screen to the Dirichlet or Neumann problems for the half-space (or the half-plane in the two-dimensional case) and permits immediately writing out an approximate analytical solution. The present paper is the first to generalize this approach to elastic wave diffraction. We use the problem of diffraction of a shear SH-wave by a half-plane to show that the Kirchhoff theory gives a good approximation to the exact solution. The discrepancies mainly arise near the screen, i.e., in the region where the influence of the boundary conditions is maximal.
Keywords elastic wave, diffraction, Kirchhoff theory
References
1.  M. Born and E. Wolf, Principles of Optics (Pergamon Press, London, 1959; Nauka, Moscow, 1973).
2.  H. Hönl, A. Maue, and K. Westphal, Theorie der Beugung (Springer, Berlin, 1961; Mir, Moscow, 1964).
3.  H. Poincare, Theorie Matematique de la Lumiere, Vol. 2 (Georges Carre Editeur, Paris, 1892).
4.  J. Nye, K. Hannay, and W. Liang, "Diffraction by a Black Half-Plane: Theory and Observation," Proc. Roy. Sci. London. Ser. A 449, 515-535 (1995).
5.  M. H. Israilov, Dynamic Theory of Elasticity and Wave Diffraction (Izdat. MGU, Moscow, 1992) [in Russian].
6.  J. A. Hudson, The Excitation and Propagation of Elastic Waves (Cambridge Univ. Press, Cambridge, 1980).
7.  M. Abramowitz and I. A. Stegun (Editors), Handbook of Mathematical Functions (Dover, New York, 1965; Nauka, Moscow, 1979).
8.  L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice Hall, New Jersey, 1972; Mir, Moscow, 1978).
9.  S. E. Nosov, "Diffraction at a Half-Plane (Antiplane Problem)," in Elasticity and Inelasticity (Izdat. MGU, Moscow, 2011), pp. 418-420 [in Russian].
Received 29 August 2014
Link to Fulltext
<< Previous article | Volume 52, Issue 1 / 2017 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100