High frequency scattering by a second-order generalized impedance discontinuity on a cylindrically curved surface

Abstract

The aim of the present paper is to obtain explicit asymptotic expressions for the "transfer (diffraction) coefficients" related to the diffraction of high frequency cylindrical waves from the discontinuity occurred in the material properties as well as in the thicknesses of a coated cylindrically curved metallic sheet characterized by the second order GIBCs. Relying on the locality of the high frequency diffraction phenomenon, the angular interval φ ∈ (-π, π) is extended to the abstract infinite space φ ∈ (-∞, ∞) wherein the diffracting structure is replaced by a two-part cylindrically curved second order impedance sheet ρ = a extending from φ = -∞ to φ = ∞. The resulting boundary value problem is formulated as a Hilbert equation which is solved asymptotically in the high frequency limit. Some graphical results showing the effects of various parameters on the transfer coefficients are presented.