Limits of slow sound propagation and transparency in lossy, locally resonant periodic structures

G Theocharis,A Merkel,O Richoux,V Tournat,V Romero García

doi:10.1088/1367-2630/16/9/093017

Abstract

We investigate sound propagation in lossy, locally resonant periodic structures by studying an air-filled tube periodically loaded with Helmholtz resonators and taking into account the intrinsic viscothermal losses. In particular, by tuning the resonator with the Bragg gap in this prototypical locally resonant structure, we study the limits and various characteristics of slow sound propagation. While in the lossless case the overlapping of the gaps results in slow-sound-induced transparency of a narrow frequency band surrounded by a strong and broadband gap, the inclusion of the unavoidable losses imposes limits to the slowdown factor and the maximum transmission. Experiments, theory, and finite element simulations have been used for the characterization of acoustic wave propagation by tuning the Helmholtz/Bragg frequencies and the total amount of loss both for infinite and finite lattices. This study contributes to the field of locally resonant acoustic metamaterials and slow sound applications.

Highlights

Resonant periodic structures exhibit two types of band gaps in their dispersion relation: the resonator and Bragg gaps
We start by studying the coupling between the Bragg and resonator gaps, taking into account viscothermal losses
We tune the resonant frequency with the Bragg frequency by experimentally calculating the dependence of the imaginary part of the complex dispersion relation on the length of the cavity, lc, of the Helmholtz resonators (HRs) (see figure 2(e))

Summary

Introduction

Resonant periodic structures exhibit two types of band gaps in their dispersion relation: the resonator and Bragg gaps. In the case of the exact overlap, the lossless theory predicts a strong and broadband gap This phenomenon has been studied in different branches of physics, including elastic waves [3], split-ring microwave propagation [4], and duct acoustics [5], among others. It is even more interesting when these two different types of gaps do not exactly overlap, but are detuned to be very close to each other. In this case, ignoring again the losses, the theory predicts an almost-flat propagating band which is very attractive for slow wave applications

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Conclusion