 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
|
| In English (Mech. Solids): | | 3212 |
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| << Previous article | Volume 48, Issue 3 / 2013 | Next article >> |
| M.Sh. Israilov, "Diffraction of Acoustic and Elastic Waves on a Half-Plane for Boundary Conditions of Various Types," Mech. Solids. 48 (3), 337-347 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
3 |
Pages |
337-347 |
| DOI |
10.3103/S0025654413030102 |
| Title |
Diffraction of Acoustic and Elastic Waves on a Half-Plane for Boundary Conditions of Various Types |
| Author(s) |
M.Sh. Israilov (Academician Millionschikov Grozny State Oil Institute, A. Avtorkhanova 14/53, Groznyy, Chechenskaya resp., 364052 Russia, israiler@hotmail.com) |
| Abstract |
The classical problem of wave diffraction on a half-plane with boundary conditions of different types and its generalizations to elastic media are considered. As a solution method it is proposed to combine the Fourier method of separation of variables and the series summation technique based on the use of integral representations of Bessel functions. The analytic solutions thus obtained are equally efficient in the near- and far-field diffraction regions. The two-term singularity at a corner point (in stresses for elastic media and in the velocity for acoustic media) was discovered for the first time. The knowledge of singularities in the scalar problem allowed one to construct the solution of the vector problem of elastic longitudinal wave diffraction. It is investigated how different types of boundary conditions on both sides of the half-plane affect the solution behavior in the far-field region. Possible physical interpretations of the obtained results are given. |
| Keywords |
diffraction, acoustic wave, elastic wave, boundary conditions of various types |
| References |
| 1. | A. D. Rawlins,
"The Solution of a Mixed Boundary-Value Problem in the Theory of Diffraction by a
Semi-Infinite Plane,"
Proc. Roy. Sci. London. Ser. A
346 (1647), 469-484 (1975). |
| 2. | R. A. Hurd,
"The Wiener-Hopf-Hilbert Method for Diffraction Problems,"
Canad. J. Phys.
54 (7), 775-780 (1976). |
| 3. | G. R. Wickham,
"Mode Conversion, Corner Singularities, and Matrix Wiener-Hopf Factorization in Diffraction Theory,"
Proc. Roy. Sci. London. Ser. A
451, 399-423 (1995). |
| 4. | F. G. Friedlander,
Sound Pulses
(Cambridge Univ. Press, Cambridge, 1958; Izd-vo Inostr. Lit., Moscow, 1962). |
| 5. | M. Sh. Israilov,
Dynamic Theory of Elasticity and Wave Diffraction
(Izd-vo MGU, Moscow, 1992)
[in Russian]. |
| 6. | A. S. Peters and J. J. Stoker,
"A Uniqueness Theorem and a New Solution for Sommerfeld's and Other Diffraction Problems,"
Comm. Pure Appl. Math.
7 (3), 565-585 (1954). |
| 7. | H. Bateman and A. Erdelyi,
Higher Transcendental Functions, Vol. 2
(McGraw-Hill, New York, 1953). |
| 8. | J. D. Murray,
Asymptotic Analysis
(Springer, New York, 1984). |
| 9. | M. H. Holmes,
Introduction to Perturbation Methods
(Springer, New York, 1995). |
| 10. | M. Born and E. Wolf,
Principles of Optics
(Pergamon Press, London, 1959). |
| 11. | V. D. Kupradze,
Dynamical Problems in Elasticity
(North-Holland, Amsterdam, 1963). |
|
| Received |
30 April 2010 |
| Link to Fulltext |
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