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Diffraction of a Plane Acoustic Wave by Eight Equal Coaxial Circular Infinite Soft Strips

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The subject of this paper is the problem of diffraction of a time harmonic obliquely incident plane acoustic wave by eight equal coaxial circular infinite soft strips. A simple independent integral equation technique is presented here to solve this two-dimensional Dirichlet boundary value problem by the standard perturbation method when the wavelength of the incident wave is very large compared to the radius of the circular strips. Approximate expressions are obtained for the farfield amplitude and the scattering cross section. By taking appropriate limits in our analysis, approximate expressions for these physical quantities of interest are derived for the corresponding limiting problem of four equal coaxial circular infinite soft strips which agree with the known results.

Zusammenfassung

Gegenstand dieser Arbeit ist das Problem der Beugung einer harmonischen, ebenen Schallwelle schräger Inzidenz durch acht gleiche, kreisförmige und koaxiale, unendliche schallweiche Streifen. Es wird eine einfache Integralgleichungsmethode zur Lösung dieses zweidimensionalen Dirichlet-Problems vorgestellt, wobei eine Standard-Störungsmethode für den Grenzfall benutzt wird, daß die Wellenlänge der einfallenden Welle sehr groß im Vergleich mit dem Radius der kreisförmigen Streifen ist. Es werden Näherungsausdrücke für die Fernfeldamplitude und den Streuquerschnitt erhalten. Durch Einführung angemessener Grenzen der Untersuchung werden für diese physikalischen Größen Näherungsausdrücke für das entsprechende Grenzproblem vier gleicher, kreisförmiger, schallweicher Streifen abgeleitet, die mit den bekannten Ergebnissen übereinstimmen.

Sommaire

On s'est poséle problème de la diffraction d'une onde acoustique plane et harmonique tombant sous incidence oblique sur un ensemble de huit bandes circulaires coaxiales faites en une matière parfaitement molle. Il s'agit d'un problème bidimensionnel de Dirichlet à valeurs aux limites. On le traite par une technique simple d'équation intégrate indépendante fournie par la méthode standard des perturbations en supposant que la longueur d'onde de l'onde incidente est très grande par rapport au rayon des bandes diffringentes. On a calculé des expressions approchées pour l'amplitude du champ diffracté à grande distance et pour la section efficace de diffraction. En choisissant des conditions aux limites appropriées, on a obtenu également ces expressions pour le problème correspondant restreint à quatre bandes et vérifié que les résultats sont en accord avec des publications antérieures.
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Document Type: Research Article

Publication date: July 1, 1991

More about this publication?
  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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