Acoustic scattering by a circular semi-transparent conical surface

Abstract

The scattering of a plane acoustic wave by a circular semi-transparent conical surface with impedancetype 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.

Scattering of a plane electromagnetic wave by a hollow circular cone with thin semi-transparent walls

“…In this section, we execute a numerical procedure for computation of the diffraction coefficients for domain ω ∈ M 1 . It is similar to that reported in Lyalinov & Zhu (2007) and Bernard et al (2008)) with appropriate modifications wherever necessary.…”

“…By the present time, an essential progress has been achieved in diffraction by cones with ideal or perfect boundary conditions, both in acoustical and in electromagnetic settings (see, e.g. Felsen, 1957;Jones, 1964Jones, , 1997Borovikov, 1966;Cheeger & Taylor, 1982;Smyshlyaev, 1989aSmyshlyaev, ,b, 1990Smyshlyaev, , 1993Babich et al, 1995, 1996, 2000, 2004, Babich, 2006Blume & Uschkerat, 1995;Blume & Krebs, 1998;Kamotskii, 1999;Klyubina, 2002;Bonner et al, 2005;Shanin, 2005;Klinkenbusch, 2007;Skelton et al, 2010) Since 1997 (Bernard, 1997), there has been a growing number of publications dealing with diffraction by cones with non-perfect (impedance-type) boundary conditions (Bernard & Lyalinov, 2001a,b, 2004Antipov, 2002;Lyalinov, 2003Lyalinov, , 2009Lyalinov, , 2010Lyalinov & Zhu, 2007). The present paper develops the SCATTERING OF A PLANE ELECTROMAGNETIC WAVE BY A HOLLOW CIRCULAR CONE latter line by studying a particular problem of diffraction by a hollow circular cone with impedancesheet boundary conditions.…”

Diffraction by a Wedge or by a Cone With Impedance-Type Boundary Conditions and Second-Order Functional Difference Equations

“…Its unique solvability will be then studied and the expression for the scattering amplitude of the spherical wave from the vertex be discussed. This section is based on [3,4,6,16]. We note that a similar analysis is presented in [5] in which numerical results for axial incidence are given and therefore, will be called upon for comparison purposes.…”

Diffraction by an elongated body of revolution. A boundary integral equation based on the parabolic equation

“…Third, for conical obstacles (with not necessarily circular cross-section) one can apply methods which are specifically conical. They are based either on Smyshlyaev's formula [11,12] or on Kontorovich-Lebedev integral representation [13,14].…”