A two-way model for nonlinear acoustic waves in a non-uniform lattice of   Helmholtz resonators
  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. 
Jean-Fran\c{c}ois Mercier (POEMS), Bruno Lombard (OandI, LMA)
physics.class-ph