Nonlinear Membrane-Type Acoustic Metamaterials: Harmonic generation and solitons, by Jiangyi Zhang (Laboratoire d’Acoustique de l’Université du Maine, UMR 6613 CNRS)
DENORMS Action’s Workshop “Modelling of high performance acoustic structures Porous media, metamaterials and sonic crystals”, Rome, 24-25th January 2017
Session on Use of metamaterials in other fields of Physics and metamaterials exposed to multiple physical phenomena
Speaker: Jiangyi Zhang (Laboratoire d’Acoustique de l’Université du Maine, UMR 6613 CNRS)
Acoustic metamaterials have been exploited during the last years in the regime of the linear propagation. However, in reality there are a lot of situations in which the sound level is so high that the propagation cannot be treated as linear. In this work we propose to extend the previous linear studies in the nonlinear regime, considering high amplitude acoustic waves in an acoustic metamaterial which consists of an air filled tube periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear dispersive wave equation. By applying perturbation method, we first study the second-harmonic generation. In this case, we pay attention to the dispersion introduced by the local resonances of the elastic plates in order to manage the different generated harmonics. Secondly, by applying the multiple scale perturbation method, we show that the propagation in this system can be described by a Nonlinear Schrödinger equation. In this case, we derive the analytical expressions for different types of envelope solitons and study the effect of viscothermal losses. Our analytical results are in good agreement with the numerical simulations and provide many opportunities for the development of nonlinear phenomena in periodic acoustic structures.