Homogenization of the acoustic transmission through a perforated layer

Rohan, Eduard; Lukeš, Vladimír

doi:10.1016/j.cam.2009.08.059

Cited by 26 publications

(39 citation statements)

References 8 publications

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“…Higher order conditions have been derived in [7] and [8] for the Laplace problem and in [9,10] for the Helmholtz equation. The case of approximate transmission conditions has been studied in [11,12] for perforated thin conductors and [13] for dielectric thin periodic layers for the Laplace equation: in [11] the two first terms of the asymptotic expansion of the solution has been obtained. The case of effective transmission conditions modeling highly conductive thin sheets is treated in [14].…”

Section: Introductionmentioning

confidence: 99%

Approximate models for wave propagation across thin periodic interfaces

Delourme

Haddar

Joly

2012

Journal de Mathématiques Pures et Appliquées

101

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This work deals with the scattering of acoustic waves by a thin ring that contains regularly spaced inhomogeneities. We first explicit and study the asymptotic of the solution with respect to the period and thickness of the inhomogeneities using so-called matched asymptotic expansions. We then build simplified models replacing the thin ring with Approximate Transmission Conditions that are accurate up to third order with respect to the layer width. We pay particular attention to the study of these approximate models and the quantification of their accuracy. RésuméCet article traite de la diffraction d'une onde acoustique par un structure constituée d'un anneau mince de diélectrique contenant un grand nombre d'hétérogénéités disposées périodiquement. On commence par écrire et justifier un développement asymptotique de la solution en fonction de l'épaisseur de l'anneau et de la distance entre les hétérogénéités. Puis, on construit des modèles approchés stables et bien posés d'ordres 2 et 3 dans lesquels l'anneau périodique est remplacé par une condition de transmission.

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Section: Introductionmentioning

confidence: 99%

Approximate models for wave propagation across thin periodic interfaces

Delourme

Haddar

Joly

2012

Journal de Mathématiques Pures et Appliquées

101

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“…A review of the bibliography published during the last years shows the rise of multidimensional techniques [1][2][3][4][5][6][7][8][9] to characterize the acoustic behavior of silencers in comparison with one-dimensional techniques, due to their higher accuracy in the silencer operating frequency range.…”

Section: Introductionmentioning

confidence: 99%

Point collocation scheme in silencers with temperature gradient and mean flow

Denia

Sánchez-Orgaz

Baeza

et al. 2016

Journal of Computational and Applied Mathematics

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This work presents a mathematical approach based on the point collocation technique to compute the transmission loss of perforated dissipative silencers with transversal temperature gradients and mean flow. Three-dimensional wave propagation is considered in silencer geometries with arbitrary, but axially uniform, cross section. To reduce the computational requirements of a full multidimensional finite element calculation, a method is developed combining axial and transversal solutions of the wave equation. First, the finite element method is employed in a two-dimensional problem to extract the eigenvalues and associated eigenvectors for the silencer cross section. Mean flow as well as transversal temperature gradients and the corresponding thermal-induced material heterogeneities are included in the model. In addition, an axially uniform temperature field is taken into account, its value being the inlet/outlet average. A point collocation technique is then used to match the acoustic fields (pressure and axial acoustic velocity) at the geometric discontinuities between the silencer chamber and the inlet and outlet pipes. Transmission loss predictions are compared favorably with a general three-dimensional finite element approach, offering a reduction in the computational effort.

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“…The homogenization problem of this contribution has also been investigated in the more mathematical work [9]. In formula (29) of that work, an effective transmission condition for p is derived (which seems curious since we derive trivial transmission conditions for p in the work at hand).…”

Section: The Homogenization Results Of Rohan and Lukešmentioning

confidence: 99%

“…In this formula, ρ denotes the density, ω the frequency, ν a normal vector on Γ 0 , pointing into the domain Ω + , and Z is a complex number, the transmission impedance, a parameter that characterizes the effective behavior of the obstacles (we cite from equation (2) of [9], where reference is given to [4]). Let us compare the empirical formula (1.2) with our findings.…”

Section: Effective Description Of the Acoustic Properties Of A Performentioning

confidence: 99%

Transmission Conditions for the Helmholtz-Equation in Perforated Domains

2016

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We study the Helmholtz equation in a perforated domain Ω ε . The domain Ω ε is obtained from an open set Ω ⊂ R 3 by removing small obstacles of typical size ε > 0, the obstacles are located along a 2-dimensional manifold Γ 0 ⊂ Ω. We derive effective transmission conditions across Γ 0 that characterize solutions in the limit ε → 0. We obtain that, to leading order O(ε 0 ) = O(1), the perforation is invisible. On the other hand, at order O(ε 1 ) = O(ε), inhomogeneous jump conditions for the pressure and the flux appear. The jumps can be characterized without cell problems by elementary expressions that contain the ε 0 -order limiting pressure function and the volume of the obstacles.

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Homogenization of the acoustic transmission through a perforated layer

Cited by 26 publications

References 8 publications

Approximate models for wave propagation across thin periodic interfaces

Approximate models for wave propagation across thin periodic interfaces

Point collocation scheme in silencers with temperature gradient and mean flow

Transmission Conditions for the Helmholtz-Equation in Perforated Domains

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