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A two-way model for nonlinear acoustic waves in a non-uniform lattice of Helmholtz resonators

Jean-François Mercier 1, * Bruno Lombard 2
* Corresponding author
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
2 O&I - Ondes et Imagerie
LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
Abstract : Propagation of high amplitude acoustic pulses is studied in a 1D waveguide connected to a lattice of Helmholtz resonators. An homogenized model has been proposed by Sugimoto (J. Fluid. Mech., \textbf{244} (1992)), taking into account both the nonlinear wave propagation and various mechanisms of dissipation. This model is extended here to take into account two important features: resonators of different strengths and back-scattering effects. An energy balance is obtained, and a numerical method is developed. A closer agreement is reached between numerical and experimental results. Numerical experiments are also proposed to highlight the effect of defects and of disorder.
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https://hal.archives-ouvertes.fr/hal-01312801
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Submitted on : Wednesday, April 5, 2017 - 1:49:07 PM
Last modification on : Friday, December 3, 2021 - 11:34:05 AM
Long-term archiving on: : Thursday, July 6, 2017 - 1:33:20 PM

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Jean-François Mercier, Bruno Lombard. A two-way model for nonlinear acoustic waves in a non-uniform lattice of Helmholtz resonators. Wave Motion, Elsevier, 2017, 72, pp.260-275. ⟨10.1016/j.wavemoti.2017.04.004⟩. ⟨hal-01312801v3⟩

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