Acoustic solitons in waveguides with Helmholtz resonators: transmission line approach

TL;DR

This paper investigates the formation and propagation of acoustic solitons in waveguides with Helmholtz resonators using a transmission-line model, combining theoretical analysis, numerical simulations, and experimental validation.

Contribution

It introduces a nonlinear lattice model for acoustic waveguides with Helmholtz resonators and derives multiple soliton solutions, validated by experiments and simulations.

Findings

Analytical soliton solutions match numerical simulations.

Experimental results confirm theoretical predictions.

Multiple types of acoustic solitons are identified.

Abstract

We report experimental results and study theoretically soliton formation and propagation in an airfilled acoustic waveguide side loaded with Helmholtz resonators. Our theoretical approach relies on a transmission-line description of this setting, which leads to a nonlinear dynamical lattice model. The latter is treated analytically, by means of dynamical systems and multiscale expansion techniques, and leads to various soliton solutions for the pressure. These include Boussinesq-like and Korteweg-de Vries pulse-shaped solitons, as well as nonlinear Schr\"{o}odinger envelope solitons. The analytical predictions are in excellent agreement with direct numerical simulations and in qualitative agreement with the experimental observations.