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
arXiv:
images/icons/icon_arxiv.png 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 },
    journal={Wave Motion },
    year={2017 },
    volume={72 },
    pages={260--275},
}