Journal of Engineering Mathematics

, Volume 59, Issue 4, pp 385–398 | Cite as

Acoustic scattering by a circular semi-transparent conical surface

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Abstract

The scattering of a plane acoustic wave by a circular semi-transparent conical surface with impedance-type boundary conditions is studied. The analytic solution is constructed on the basis of the incomplete separation of variables and the reduction of the problem to a functional difference equation of the second order. Although the latter is equivalent to a Carleman boundary-value problem for analytic vectors, the solution is studied by means of the direct reduction method, that is, converting the functional difference equations to a Fredholm-type integral equation. Its unique solvability is then studied and the expression for the scattering amplitude of the spherical wave from the vertex is discussed. Some numerical results for axial incidence are also presented.

Keywords

Carleman problems Fredholm integral equation Functional difference equation Scattering amplitude Wiener–Hopf 
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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Mathematical Physics, Institute of PhysicsSaint-Petersburg UniversityPetershofRussia
  2. 2.Institut für HochfrequenztechnikUniversität StuttgartStuttgartGermany

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