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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 1995 Volume 221, Pages 67–74 (Mi znsl4296)

This article is cited in 3 papers

Diffraction of a plane wave by a narrow cone

V. M. Babicha, B. A. Samokishb, D. B. Dement'evc

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b St. Petersburg State University of Architecture and Civil Engineering
c Saint-Petersburg State University

Abstract: The problem of diffraction of a plane scalar wave by a narrow cone is considered. The shape of the cone is arbitrary. The boundary condition is the Dirichlet or Neumann one. The wave scattered by the cone vertex arises as a result of the diffraction process. The subject of this paper is to calculate the wave amplitude. If the cone is narrow, it is possible to obtain simpler approximate formulas in comparison with Smyshlayev's one. The exactness of the approximate formulas is checked numerically. The etalon is a solution in explicit form in the axially symmetric case. The calculation shows that our formula is more exact in the case of the Dirichlet boundary condition than Felsen's formula. The approximate formula is a generalization of Felsen's one for circular cone to an arbitrary narrow cone in the case of the Neumann boundary condition. Bibliography: 6 titles.

UDC: 517.9

Received: 20.01.1995


 English version:
Journal of Mathematical Sciences (New York), 1997, 87:2, 3311–3315

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