Iridescent Perfect Absorption in Critically-Coupled Acoustic Metamaterials Using the Transfer Matrix Method

Noé Jiménez,Jean-Philippe Groby,Vicent Romero-García,Vincent Pagneux

doi:10.3390/app7060618

Noé Jiménez, Jean-Philippe Groby + Show 2 more

Open Access

https://doi.org/10.3390/app7060618

Copy DOI

Abstract

The absorption performance of a locally-reacting acoustic metamaterial under oblique incidence is studied. The metamaterial is composed of a slotted panel, each slit being loaded by an array of Helmholtz resonators. The system is analytically studied using the transfer matrix method, accounting for the viscothermal losses both in the resonator elements and in the slits, allowing the representation of the reflection coefficient in the complex frequency plane. We show that by tuning the geometry of the metamaterial, perfect absorption peaks can be obtained on demand at selected frequencies and different angles of incidence. When tilting the incidence angle, the peaks of perfect absorption are shifted in frequency, producing an acoustic iridescence effect similar to the optic iridescence achieved by incomplete band gap. Effectively, we show that in this kind of locally-reacting metamaterial, perfect and omnidirectional absorption for a given frequency is impossible to achieve because the metamaterial impedance does not depend on the incidence angle (i.e., the impedance is a locally reacting one). The system is interpreted in the complex frequency plane by analysing the trajectories of the zeros of the reflection coefficient. We show that the trajectories of the zeros do not overlap under oblique incidence, preventing the observation of perfect and omnidirectional absorption in locally reacting metamaterials. Moreover, we show that for any locally resonant material, the absorption in diffuse field takes a maximal value of 0.951, which is achieved by a material showing perfect absorption for an incidence angle of 50.34 degrees.

Highlights

Acoustic absorption is a major topic in acoustics, mainly because acoustic absorbers are broadly used in industry
As shown in Reference [15], by tuning the geometrical parameters, the structure described in this work can be impedance matched with the exterior medium, and perfect acoustic absorption can be obtained
When the incidence angle of the incoming wave is tilted, the absorption peaks shift in frequency, producing an acoustic iridescent effect due to its selective and perfect absorption at particular angles and frequencies

Summary

Introduction

Acoustic absorption is a major topic in acoustics, mainly because acoustic absorbers are broadly used in industry (e.g., in building and civil engineering applications). In these situations, a typical configuration is to place the materials at the walls of a room, the non-reflecting acoustic material being rigidly backed. When a porous foam layer is rigidly backed, absorption might be large for frequencies only above the so-called quarter wavelength resonance of the backed layer. The main limitation of porous material-based absorbers yields in the sound speed inside the absorbers, which is on the same order as the one in the air medium: to efficiently absorb low-frequency sound, the thickness of the layer must be large, because at these frequencies the wavelength in air is on the order of several meters. Peculiar absorption properties are encountered in composite structures like double porosity

Methods

Results

Discussion

Conclusion