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Intermediate Procedures in Resonance Scattering Theory

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In the example of the steady-state scattering problem of a plane acoustic wave by a circular cylindrical shell, the expediency of including in the resonance scattering theory of intermediate stages of summation of the contributions of the same kind of modal resonance components of successive orders is demonstrated. Such a summation permits the evaluation of the contribution to the form function of the resonances with small Q factors and strongly overlapping resonance curves. For the equiphase summation of such resonances, the contribution of their superposition into the form function can be important (commensurable with the contribution of the specularly reflected wave), and for the antiphase summation, this contribution is negligibly small. As a rule, the contribution of the superposition of the equiphase resonances can be clearly observed in the form function curve, while the contribution of a single resonance with small Q factor is practically not noticeable on it.

Zusammenfassung

Anhand der stationären Streuung einer ebenen Schallwelle an einer kreiszylindrischen Schale wird die Nützlichkeit von Zwischenschritten in der Theorie der Resonanzstreuung demonstriert, die aus einer Summation gleichartiger Beiträge modaler Resonanzkomponenten immer höherer Ordnung besteht. Eine derartige Summation erlaubt die Ermittlung der Beiträge zur Formfunktion der Resonanzen mit kleinem Q-Faktor und stark über-lappenden Resonanzkurven. Bei gleichphasiger Summation können solche Resonanzen einen bedeutenden Beitrag zu der Formfunktion leisten (was mit dem Beitrag der geometrisch reflektierten Welle kommensurabel ist); bei gegenphasiger Summation wird dieser Beitrag dagegen verschwindend klein. In der Regel kann der Beitrag der Überlagerung gleichphasiger Resonanzen in der Kurve der Formfunktion deutlich beobachtet werden, während der Beitrag einer einzelnen Resonanz mit kleinem Q-Faktor praktisch unmerklich ist.

Sommaire

En prenant comme exemple le problème de la diffusion en régime permanent d'une onde acoustique plane par une coque cylindrique à section circulaire, nous démontrons la rentabilité de l'emploi, en théorie de la diffusion résonante, d'étapes intermédiaires de sommation des contributions de composantes modales de résonance de même type pour les ordres successifs. Une telle sommation permet d'évaluer la contribution à la fonction de forme des résonances à faible facteur Q et dont les courbes de résonance se chevauchent en grande partie. La sommation de telles résonances en concordance de phase peut produire une contribution importante à la fonction de forme (comparable à la contribution de la réflexion spéculaire) tandis que la sommation en opposition de phase ne donne qu'une contribution négligeable. En règie générate, la contribution apportée à la fonction de forme par la superposition des résonances en concordance de phase peut être nettement observable, alors que la contribution d'une résonance isolée, à faible valeur de Q, passé pratiquement inaperçue.
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Document Type: Research Article

Publication date: January 1, 1994

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  • 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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