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Diffusive series representation for the Crandall model of acoustic impedance.

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Title: Diffusive series representation for the Crandall model of acoustic impedance.
Authors: Drozda, Luciano1 (AUTHOR) drozda@cerfacs.fr, Matignon, Denis2 (AUTHOR)
Source: Meccanica. Apr2023, Vol. 58 Issue 4, p555-564. 10p.
Subjects: Acoustic models, Bessel functions, Transcendental functions, Acoustic impedance, Impulse response, Porous materials
Abstract: Porous media used in soundproofing systems can be modeled as a set of cylindrical perforations. Starting from the classical expression of the acoustic impedance of cylindrical tubes which is proportional to a ratio of Bessel functions, this paper briefly presents the derivation of an equivalent expression depending only on the positive zeros of J 2 , the Bessel function of the first kind of order 2. In the frequency domain, such a derivation is of great practical interest because it replaces the costly evaluation of transcendental functions by that of rational ones. In the time domain, the impulse response of the cylindrical tube reduces to a Prony series of which only 10 terms prove sufficient to reliably describe it, for any values of physical parameters within the acoustic model assumptions. The method applied in this use case from acoustics was primarily employed by Giusti and Mainardi (Meccanica 51(10): 2321–2330, 2016) in their study of pulse propagation within blood vessels and by Colombaro et al. (Meccanica 52(4–5):825–832, 2017) in their work on the Bessel models of linear viscoelasticity. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:Porous media used in soundproofing systems can be modeled as a set of cylindrical perforations. Starting from the classical expression of the acoustic impedance of cylindrical tubes which is proportional to a ratio of Bessel functions, this paper briefly presents the derivation of an equivalent expression depending only on the positive zeros of J 2 , the Bessel function of the first kind of order 2. In the frequency domain, such a derivation is of great practical interest because it replaces the costly evaluation of transcendental functions by that of rational ones. In the time domain, the impulse response of the cylindrical tube reduces to a Prony series of which only 10 terms prove sufficient to reliably describe it, for any values of physical parameters within the acoustic model assumptions. The method applied in this use case from acoustics was primarily employed by Giusti and Mainardi (Meccanica 51(10): 2321–2330, 2016) in their study of pulse propagation within blood vessels and by Colombaro et al. (Meccanica 52(4–5):825–832, 2017) in their work on the Bessel models of linear viscoelasticity. [ABSTRACT FROM AUTHOR]
ISSN:00256455
DOI:10.1007/s11012-022-01635-0