Diffraction of scalar waves by an impedance cone of arbitrary cross-section

Wave Motion

Volumn 33, Issue 2, 2001, Pages 155-181

  Bernard, J M L ^a   Lyalinov, M A ^b  

^a CEA DIF   (France)

^b ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008571094     PISSN: 01652125     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-2125(00)00055-X     Document Type: Article

References (30)

1. J. Cheeger, M.E. Taylor, Diffraction of waves by conical singularities, Commun. Pure Appl. Math. 35 (3/4) (1982) 275-331, 487-529.
2. Smyshlyaev V.P. Diffraction by conical surfaces at high frequencies. Wave Motion. 12(4):1990;329-339.
3. V.P. Smyshlyaev, On the diffraction of waves by cones at high frequencies, Preprint of LOMI, E-9-89, Leningrad, 1989.
4. V.P. Smyshlyaev, High-frequency asymptotic behavior of the Green function for the Helmholtz equation in a region with a conical boundary, Sov. Phys. Dokl. 34 (11) (1989).
5. Babich V.M., Dement'ev D.B., Samokish B.A. On diffraction of high frequency waves by a cone of arbitrary shape. Wave Motion. 21:1995;203-207.
6. Babich V.M. On diffraction of a high-frequency acoustic wave by a narrow absolutely rigid cone of an arbitrary shape. Appl. Math. Mech. 60(1):1996;72-78.
7. Babich V.M., Dement'ev D.B., Samokish B.A., Smyshlyaev V.P. On evaluation of the diffraction coefficients for arbitrary 'non-singular' directions of a smooth convex cone. SIAM Appl. Math. 60(2):2000;536-573.
8. Blume S., Uschkerat U. The radar cross-section of the semiinfinite elliptic cone - numerical evaluation. Wave Motion. 22:1995;311-326.
9. Jones D.S. Scattering by a cone. Q. J. Mech. Appl. Math. 50:1997;499-523.
10. J.M.L. Bernard, Méthode analytique et transformées fonctionnelles pour la diffraction d'ondes par une singularité conique: équation intégrale de noyau non-oscillant pour le cas d'impédance constante, Rapport CEA-R-5764, Editions Dist-Saclay, CEA/Saclay, 1997.
11. Bernard J.M.L., Lyalinov M.A. The leading asymptotic term for the scattering diagram in the problem of diffraction by a narrow circular impedance cone. J. Phys. A. 32:1999;L43-L48.
12. D.S. Jones, Acoustic and Electromatic Waves, Clarendon Press, Oxford, 1986.
13. L.B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves, Prentice-Hall, Englewood Cliffs, NJ, 1973.
14. Maliuzhinets G.D. Excitation, reflection and emission of surface waves from a wedge with given face impedances. Sov. Phys. Dokl. 3:1958;752-755.
15. G.D. Maliuzhinets, Relation between the inversion formulas for the Sommerfeld integral and the formulas of Kontorovich-Lebedev, Phys. Dokl. (1957) 266-268.
16. A.V. Osipov, On the method of Kontorovich-Lebedev's integrals for the problems of diffraction in sectorial media, in: Problems of Diffraction and Propagation of Waves, Vol. 25, St Petersburg University Publications, 1993, pp. 173-219.
17. Felsen L.B. Plane wave scattering by small-angle cones. IRE Trans. Antennas Propagation. 5:1957;121-129.
18. Keller J.B., Lewis R.M., Seckler B.D. Asymptotic solutions of some diffraction problems. Commun. Pure Appl. Math. 9:1956;207-265.
19. D.S. Jones, The Theory of Electromagnetism, Pergamon Press, London, 1964.
20. I.M. Gel'fand, G.E. Shilov, Generalized Functions, Academic Press, New York, 1964.
21. M. Abramowitz, I. Stegun, et al., Handbook of Mathematical Functions, Dover, New York, 1972.
22. A.M. Il'in, Matching the Asymptotic Expansions of the Boundary Value Problems Solutions, Nauka, Moscow, 1989.
23. W.G. Mazja, S.A. Nazarov, B.A. Plamenevski, Asymptotische Theorie Elliptischez Randwertaufgaben in Singulär Gestorten Gebieten, Academie Verlag, Berlin, 1991.
24. Maliuzhinets G.D. Inversion formula for the Sommerfeld integral. Phys. Dokl. 3:1958;52-56.
25. A. Erdelyi, et al., Tables of Integral Transforms, McGraw-Hill, New York, 1954.
26. M. Cessenat, Mathematical Method in Electromagnetism: Linear Theory and Applications, Vol. 41, World Scientific, Singapore, 1996.
27. Tuzhilin A.A. The theory of Maliuzhinets inhomogenous functional equations. Different. Urav. 9(11):1973;2058-2064.
28. I.S. Gradshteyn, I.M. Ryzhik, Tables of Integrals, Series, and Products, Academic Press, New York, 1994.
29. V.A. Borovikov, Diffraction by Polygons and Polyhedrons, Nauka, Moscow, 1966.
30. V.I. Smirnov, A Course of Higher Mathematics, Pergamon Press, Oxford, 1957.