Modelling resonant arrays of the Helmholtz type in the time domain

Agnès Maurel 1 Jean-Jacques Marigo 2 Jean-François Mercier 3 Kim Pham 2
3 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 : We present a model based on a two-scale asymptotic analysis for resonant arrays of the Helmholtz type, with resonators open at a single extremity (standard resonators) or open at both extremities (double-sided resonators). The effective behaviour of such arrays is that of a homogeneous anisotropic slab replacing the cavity region, associated with transmission, or jump, conditions for the acoustic pressure and for the normal velocity across the region of the necks. The coefficients entering in the effective wave equation are simply related to the fraction of air in the periodic cell of the array. Those entering in the jump conditions are related to near field effects in the vicinity of the necks and they encapsulate the effects of their geometry. The effective problem, which accounts for the coupling of the resonators with the surrounding air, is written in the time domain which allows us to question the equation of energy conservation. This is of practical importance if the numerical implementations of the effective problem in the time domain is sought.
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Submitted on : Monday, June 25, 2018 - 11:01:36 AM
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Agnès Maurel, Jean-Jacques Marigo, Jean-François Mercier, Kim Pham. Modelling resonant arrays of the Helmholtz type in the time domain. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2018, 474 (2210), ⟨10.1098/rspa.2017.0894⟩. ⟨hal-01822490⟩



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