Anthony D. Rawlins

The solution of a mixed boundary value problem in the theory of diffraction

SummaryAn exact solution is obtained for the problem of the diffraction of a cylindrical sound wave by an absorbent semi-infinite plane. The two faces of the half-plane have different impedance boundary conditions. The problem which is solved is a mathematical model for a noise barrier whose surface is treated with two different acoustically absorbent materials.The usual Wiener-Hopf method (which is the standard technique for solving half-plane problems) has to be modified to give a solution to the present mixed boundary value problem.

SOUND RADIATION IN A PLANAR TRIFURCATED LINED DUCT

Abstract We shall consider the radiation of the fundamental plane wave mode which propagates out of the mouth of a semi-infinite rigid waveguide. This semi-infinite waveguide is symmetrically located inside an infinite acoustically lined waveguide. The whole system constitutes a new trifurcated waveguide boundary value problem. A close form solution is obtained by the Wiener-Hopf technique. The presented solution has applications in duct acoustics and electromagnetic waveguide theory. The solution is used to give numerical results for some special situation of interest.

Diffraction from structures with an impedance boundary

A numerical study of the scattering of an E-polarised plane wave by an infinite cylindrical structure, on which an impedance boundary condition is enforced, is described. It employs an integral equation formulation for which a rapidly convergent quadrature scheme is developed. The computed scattered far-field patterns are compared with the results of Rawlins [1] for rectangular structures obtained by high frequency methods, in order to validate his solutions over the range of impedances and wavenumbers examined.

Two-dimensional diffraction by impedance loaded structures with corners

A numerical study of the scattering of an E-polarised plane wave by an infinite cylindrical structure, on which an impedance boundary condition is enforced, is described. The formulation allows structures with corners. It employs an integral equation formulation for which a rapidly convergent quadrature scheme is developed. The computed scattered near- and far-field patterns for some test objects are compared with those of the same objects with rounded corners, where the radius of curvature of the rounding is small.

DIFFRACTION BY A RIGID BARRIER WITH A SOFT OR PERFECTLY ABSORBENT END FACE

Abstract The reduction of noise levels in the shadow region of a rigid barrier of finite thickness is considered when the end face of the barrier is lined with either a soft or a perfectly absorbent material. Solutions, obtained by the method of matched asymptotic expansions, are given for both a semi-infinite barrier and for a finite length barrier placed on a rigid plane. Comparisons are made with existing solutions for barriers that have a rigid end face.

Grazing wave diffraction by a PEC or PMC rectangular cylinder

In a previous publication (B. Morse. Diffraction by polygonal cylinders. Jour Math Physics 5(2)(1964)p199) Morse used existing asymptotic results derived by Oberhettinger for wedge diffraction, to solve by the Keller method, diffraction by polygonal cylinders. In particular the PEC and PMC rectangular cylinder. For grazing incidence when the EM wave is incident along one of the side faces the normal Keller method breaks down. An alternative method was used to overcome this situation. The method used was not rigorous, in that integrals representing the diffracted field were evaluated even though they were divergent. In order to deal with an impedance cylinder the present author found the method proved unworkable and so another technique had to be used. To compare the results of the impedance cylinder in the limit of becoming a PEC or PMC I needed to be confident that the results of Morse were correct. This talk gives an alternative approach that does not involve dealing with divergent integrals to verify the results obtained by Morse.