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Influence of the neck shape for Helmholtz resonators

Jean-François Mercier 1 Jean-Jacques Marigo 2 Agnès Maurel 3 
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : The resonance of a Helmholtz resonator is studied with a focus on the influence of the neck shape. This is done using a homogenization approach developed for an array of resonators, and the resonance of an array is discussed when compared to that of a single resonator. The homogenization makes a parameter ℬ appear which determines unambiguously the resonance frequency of any neck. As expected, this parameter depends on the length and on the minimum opening of the neck, and it is shown to depend also on the surface of air inside the neck. Once these three geometrical parameters are known, ℬ has an additional but weak dependence on the neck shape, with explicit bounds.
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Submitted on : Tuesday, December 7, 2021 - 2:44:43 PM
Last modification on : Thursday, October 27, 2022 - 3:58:22 AM


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Jean-François Mercier, Jean-Jacques Marigo, Agnès Maurel. Influence of the neck shape for Helmholtz resonators. Journal of the Acoustical Society of America, 2017, 142 (6), pp.3703 - 3714. ⟨10.1121/1.5017735⟩. ⟨hal-01699681⟩



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