Second-Harmonic Generation in Acoustic Waveguides Loaded with an Array of Side Holes
Résumé
We study analytically and numerically second-harmonic generation in a one-dimensional weakly lossy nonlinear acoustic metamaterial composed of an air-filled waveguide periodically loaded by side holes. Based on the transmission line approach, we derive a lossy nonlinear dispersive lattice model which, in the continuum limit, leads to a nonlinear, dispersive and dissipative wave equation. The latter is studied by means of a perturbation method, which leads to analytical expressions for the first and second harmonics, in very good agreement with numerical results.