Acoustic solitons in waveguides with Helmholtz resonators: transmission line approach

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 Schröodinger envelope solitons. The analytical predictions are in excellent agreement with direct numerical simulations and in qualitative agreement with the experimental observations.

10 pages, 9 figures

Cited by in corpus (4)

• Structure-Composition Correspondence in Crystalline Metamaterials for Acoustic Valley-Hall Effect and Unidirectional Sound Guiding
• Acoustic solitons in a periodic waveguide: theory and experiments
• Dynamical Instability of 3d Stationary and Traveling Planar Dark Solitons
• Pitch-controlled reorientational nonlinearity in chiral nematic liquid crystals: a reduced-order model for self-focusing and soliton formation