 | | 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 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| 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 |
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