Propagation of acoustic pulses of high amplitude in a one-dimensional array of Helmholtz resonators connected to a waveguide is investigated both theoretically, numerically and experimentally. Based on the work of Sugimoto (J. Fluid. Mech., 244 (1992), 55-78), a new numerical method was developed in collaboration with B. Lombard (LMA-Marseilles) and J-F. Mercier (POEMS-Paris) taking into account both the nonlinear propagation characteristics but also the various dissipation mechanisms: linear visco-thermal losses on the walls and the nonlinear absorption due to the formation of a jet at the outlet necks of the resonators. The excellent agreement between the numerical and experimental results has highlighted the crucial role of the nonlinear absorption. Different types of solitary waves were observed experimentally with dependent characteristics of the network dispersion properties.
Experimental and numerical acoustic soliton
Furthermore, as part of a collaboration with Prof. D. Frantzeskakis of the University of Athens, a theoretical model has been proposed, using the transmission lines of approach to establish a nonlinear model of the dynamics of different types of acoustic metamaterials. This allows the analytical description of the harmonic generation and various soliton solutions using a multi-scale perturbation methods. The soliton solutions are Boussinesq type and Korteweg-de Vries, that have been observed experimentally, as well as envelope solitons described by the nonlinear Schrödinger equation.
Bright and dark solitons in acoustics