Diffraction of high-frequency waves by a cylindrically curved surface with different face impedances

Demír²

2006

Z. angew. Math. Mech.

In the present work the radiation of sound from a bifurcated circular waveguide formed by a semi‐infinite rigid duct inserted axially into a larger infinite tube with discontinous wall impedance is analyzed. The formulation of the boundary‐value problem in terms of Fourier integrals leads to a matrix Wiener‐Hopf equation which is uncoupled by the introduction of infinite sum of poles. The exact solution is then obtained in terms of the coefficients of the poles, where these coefficients are shown to satisfy infinite system of linear algebraic equations. This system is solved numerically and the influence of the parameters such as the outer cylinder radius and the discontinuity of the surface impedances on the radiation phenomenon is shown graphically.

Section: Introductionmentioning

confidence: 99%

Radiation of sound from a semi-infinite rigid duct inserted axially into a larger infinite tube with wall impedance discontinuity

Demír²

2006

Z. angew. Math. Mech.

“…For example the Wiener-Hopf-Hilbert method introduced by Hurd [1], Rawlins [2] and Rawlins and Williams [3] is powerful in the case where the kernel matrix has only branch point singularities (see, e.g. References [4][5][6]), while the Daniele-Khrapkov method proposed independently by Daniele [7] and Khrapkov [8] is e ective for a class of matrices having only pole singularities and branch point singularities besides pole singularities (see, e.g. References [9][10][11][12][13]).…”

Section: Introductionmentioning

confidence: 99%

Solution of a matrix Wiener-Hopf equation connected with the plane wave diffraction by an impedance loaded parallel plate waveguide

Çınar

2005

Math. Meth. Appl. Sci.

SUMMARYA matrix Wiener-Hopf equation connected with a new canonical di raction problem is solved explicitly. We consider the di raction of a plane electromagnetic wave by an impedance loaded parallel plate waveguide formed by a two-part impedance plane and a parallel perfectly conducting half-plane. The representation of the solution to the boundary-value problem in terms of Fourier integrals leads to a matrix Wiener-Hopf equation. The exact solution is obtained in terms of two inÿnite sets of unknown coe cients satisfying two inÿnite systems of linear algebraic equations. These systems are solved numerically and the in uence of the parameters such as the waveguide spacing and the surface impedances of the two-part plane on the di raction phenomenon is shown graphically.

“…For example, the Wiener-Hopf Hilbert method introduced by Hurd [2], Rawlins [3] and Rawlins and Williams [4] is powerful in the case where the kernel matrix has only branch point singularities (see e.g. [5][6][7]), while the Daniele-Khrapkov method proposed independently by Daniele [8] and Khrapkov [9] is effective for a class of matrices having only pole singularities and branch-cut singularities besides pole singularities (see e.g. [10][11][12][13]).…”

Section: Introductionmentioning

confidence: 99%

Scattering of plane waves by the junction of transmissive and soft-hard half-planes

Çınar

Serbest

2004

Z. angew. Math. Phys.

A uniform asymptotic high frequency solution is developed for the diffraction of plane waves by the junction of two half-planes. One of the half-planes is assumed to be characterized by "Senior's resistive-type" partially transmissive boundary conditions and the other is soft at the top and hard at the bottom. The related boundary-value problem is formulated as a matrix Wiener-Hopf equation which is solved explicitly through the Daniele-Khrapkov method. Some graphical results are also presented.