Diffraction coefficients related to cylindrically curved soft-hard surfaces

An asymptotic solution to the problem of the diffraction of high-frequency waves by the edge of a cylindrically curved surface whose convex and concave faces present soft and hard boundary conditions is obtained. The results permit us to define new diffraction coefficients related to this kind of mixed boundary conditions. When the radius of the curvature becomes infinitely large, the edgediffraction coefficient reduces to this known for the softhard half-plane.     

Diffraction of acoustic waves by a semi-infinite cylindrical impedance pipe of certain wall thickness

An asymptotic high-frequency solution is presented for the problem of diffraction of acoustic waves emanating from a ring source by a semi-infinite cylindrical pipe of certain wall thickness having different internal, external and end surface impedances. Through the application of the Fourier-transform technique in conjunction with the Mode Matching method, the diffraction problem is described by a modified Wiener–Hopf equation of the second kind and then solved approximately. Various numerical results illustrating the effects of the parameters of the problem on the diffraction phenomenon are presented.     

Transmission of sound waves in a cylindrical duct with an acoustically lined muffler

The propagation of sound in an infinite rigid cylindrical duct with an inserted expansion chamber whose walls are treated with an acoustically absorbent material is investigated rigorously through the Wiener–Hopf technique. By introducing the Fourier transform for the scattered field and applying the boundary conditions in the transform domain, the problem is reduced into a modified Wiener–Hopf equation. The solution involves four sets of infinitely many constants satisfying four infinite systems of linear algebraic equations. An approximate solution of these systems is obtained by means of numerical procedures.     

Scattering of the TEM mode at the junction of perfectly conducting and impedance coaxial waveguides

In the present work, a rigorous Wiener?CHopf approach is used to investigate the radiation characteristics of a two-part coaxial waveguide, whose left part is perfectly conducting while the surface impedances of the inner and outer cylinders of the right part are different from each other. The representation of the solution to the boundary-value problem in terms of Fourier integrals leads to two simultaneous modified Wiener?CHopf equations whose formal solution is obtained by using the factorization and decomposition procedures. The solution involves two infinite sets of unknown coefficients satisfying two infinite systems of linear algebraic equations. These systems are solved numerically, and some graphical results showing the influence of the spacing between the coaxial cylinders and the surface impedances on the reflection coefficient are presented.     

Multiple diffraction of plane waves by a soft/hard strip

A uniform asymptotic high-frequency solution is developed for the problem of diffraction of plane waves by a strip which is soft at one side and hard on the other. The related three-part boundary value problem is formulated into a modified matrix Wiener-Hopf equation. By using the known factorization of the kernel matrix through the Daniele-Khrapkov method, the modified matrix Wiener-Hopf equation is first reduced to a pair of coupled Fredholm integral equations of the second kind and then solved by iterations. An interesting feature of the present solution is that the classical Wiener-Hopf arguments yield unknown constants which can be determined by means of the edge conditions.Also with Tübitak Marmara Research Center, Department of Mathematics, 41740 Gebze, Kocaeli, Turkey     

Diffraction by a rectangular groove with resistive walls

The plane wave diffraction from a rectangular groove having resistive vertical walls with material loading is analyzed for E polarization by using the Fourier transform technique. The problem is formulated into a modified Wiener–Hopf equation applying boundary conditions. The modified Wiener–Hopf equation is solved via the factorization and decomposition procedure. The scattered field is evaluated by taking the inverse Fourier transform and applying the saddle point method. Numerical results on the backscatter radar cross-section (RCS) patterns are presented for various physical parameters.     

Plane wave diffraction by a slit in a perfectly conducting plane and a parallel complementary strip

The diffraction of plane electromagnetic waves by the configuration formed by a slit in a perfectly conducting plane and a parallel complementary strip is investigated. The related boundary-value problem is formulated into a modified matrix Wiener-Hopf equation. The factorization of the kernel matrix is accomplished through Abrahams’ method and the modified matrix Wiener-Hopf equation is first reduced to a pair of coupled Fredholm integral equations of the second kind and then solved by iterations. Several numerical results illustrating the effects of various parameters such as the spacing between the slit and the strip and their width on the diffraction phenomena are presented.     

Radiation of sound waves from a rigid stepped cylindrical waveguide

The radiation of plane harmonic sound waves from a rigid stepped cylindrical waveguide is treated by using the mode-matching method in conjunction with theWiener-Hopf technique. The solution is exact, but formal, since infinite series of unknowns and some branch-cut integrals with unknown integrands are involved. Approximation procedures based on rigorous asymptotics are used and the approximate solution to the Wiener-Hopf equations is derived in terms of infinite series of unknowns, which are determined from infinite systems of linear algebraic equations. Numerical solutions of these systems are obtained for various values of the parameters of the problem and their effects on the directivity of the stepped waveguide is presented.     

Plane wave diffraction by the discontinuity formed by resistive and impedance half-planes : oblique incidence case

The problem of plane wave diffraction from a plane discontinuity formed by impedance and resistive half-planes is considered for the oblique incidence case. This two-part mixed boundary value problem is formulated by a set of equivalent boundary conditions expressed in terms of normal components of the field and their normal derivatives. Thus the problem is reduced to a set of scalar Wiener-Hopf equations which are easily solved by standard techniques. Then, diffracted field expressions are derived asymptotically for k→∞, and it is shown that they reduce to the known results related to the normal incidence case.

     

Diffraction of plane waves by a resistive strip residing between two impedance half-planes

A uniform asymptotic solution is presented for the diffraction of E_z polarized plane waves by a resistive strip residing between two impedance half-planes. The analysis proceeds from triple integral equations approach which leads to a system of uncoupled modified Wiener-Hopf equations (MWHE). This system is then reduced to two pairs of Fredholm integral equations of the second kind which are solved by successive approximations. Diffracted field expressions are derived up to the third order terms which include the surface wave field effects in a uniform manner.