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

TL;DR

This paper extends a nonlinear acoustic wave model in a lattice of Helmholtz resonators to include variable resonator strengths and back-scattering, improving agreement with experiments and exploring defect effects.

Contribution

The authors develop an extended homogenized model that incorporates resonator variability and back-scattering, enhancing the understanding of nonlinear wave propagation in non-uniform resonator lattices.

Findings

Improved numerical and experimental agreement.

Effect of defects and disorder analyzed.

Energy balance established for the extended model.

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.