Nonlocal description of sound propagation through an array of Helmholtz resonators

TL;DR

This paper applies a nonlocal macroscopic theory of sound propagation to an array of Helmholtz resonators, demonstrating its ability to describe resonance effects and metamaterial properties like negative bulk modulus.

Contribution

It extends the nonlocal theory to complex resonator arrays, validating it through calculations of Bloch wavenumber and bulk modulus in periodic structures.

Findings

The nonlocal theory accurately predicts frequency-dependent properties.

Resonance effects are effectively modeled in Helmholtz resonator arrays.

Metamaterial properties such as negative bulk modulus are confirmed.

Abstract

A generalized macroscopic nonlocal theory of sound propagation in rigid-framed porous media saturated with a viscothermal fluid has been recently proposed, which takes into account both temporal and spatial dispersion. Here, we consider applying this theory capable to describe resonance effects, to the case of sound propagation through an array of Helmholtz resonators whose unusual metamaterial properties such as negative bulk moduli, have been experimentally demonstrated. Three different calculations are performed, validating the results of the nonlocal theory, relating to the frequency-dependent Bloch wavenumber and bulk modulus of the first normal mode, for 1D propagation in 2D or 3D periodic structures.