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

Jean-François Mercier and Bruno Lombard

2017

Publication type:

Paper in peer-reviewed journals

Journal:

Wave Motion, vol. 72, pp. 260-275

Publisher:

Elsevier

DOI:

10.1016/j.wavemoti.2017.04.004

HAL:

hal-01312801

arXiv:

1609.03841

Keywords :

Helmholtz resonators; Burgers equation; nonlinear acoustics; fractional derivatives; solitons; diffusive representation;

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.

BibTeX:

@article{Mer-Lom-2017,
    author={Jean-François Mercier and Bruno Lombard },
    title={A two-way model for nonlinear acoustic waves in a non-uniform 
           lattice of Helmholtz resonators },
    doi={10.1016/j.wavemoti.2017.04.004 },
    journal={Wave Motion },
    year={2017 },
    volume={72 },
    pages={260--275},
}