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

Jean-François Mercier; Bruno Lombard

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arXiv · 1609.03841

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

Jean-François Mercier·Bruno Lombard

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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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Jean-François Mercier, Bruno Lombard. 2016-09-13. A two-way model for nonlinear acoustic waves in a non-uniform lattice of Helmholtz resonators. https://arxiv.org/abs/1609.03841

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