  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.
