Thermoviscous-acoustic metamaterials to damp acoustic modes in complex shape geometries at low frequencies.

Tenon Charly Kone,Maël Lopez,Sebastian Ghinet,Thomas Dupont,Raymond Panneton

doi:10.1121/10.0006441

Abstract

This article proposes a hybrid numerical-analytical approach to effectively predict the sound absorption coefficient of complex periodic metamaterials with a reasonably low computation time. A variation of an existing metamaterial, consisting of a periodic succession of necks and cavities, is also proposed. The design variation was intended to decrease the frequencies of the absorption coefficient resonant peaks and consists in adding eccentricity in the neck position. The hybrid approach combines a thermoviscous-acoustic (TVA) approach with the transfer matrix (TM) method. The TVA approach estimates the thermoviscous losses of acoustic waves in a periodic unit cell (PUC) of the metamaterial. The TM method is used to simulate the acoustic behaviour of the complete metamaterial from the TM of the PUC calculated numerically. The approach is compared to impedance tube measurements on prototypes of the metamaterial. The comparison shows that the proposed approach is in good agreement with the measured sound absorption coefficient. In addition, numerical simulations and experiments demonstrate that the proposed variation of the existing metamaterial results in a shift of the absorption peaks down in frequency without deteriorating their sound absorption performance.

Highlights

This article proposes a hybrid numerical-analytical approach to effectively predict the sound absorption coefficient of complex periodic metamaterials with a reasonably low computation time
The TVA approach estimates the thermoviscous losses of acoustic waves in a periodic unit cell (PUC) of the metamaterial
One of the main objectives of this study is to develop metamaterials with complex geometries capable to effectively attenuate the acoustic waves at low frequencies within a limited available physical integration volume

Summary

Introduction

This article proposes a hybrid numerical-analytical approach to effectively predict the sound absorption coefficient of complex periodic metamaterials with a reasonably low computation time. In Ref. 11, it was proposed to model the resonant material with periodically spaced dead-end cavities by a transfer matrix method (TMM) with a low frequency asymptotic approach. The equivalent fluid model, such as the Johnson-ChampouxAllard (JCA) model, was used to account for thermoviscous losses in the metamaterials by calculating an effective dynamic density and bulk modulus (compressibility) for the air in the metamaterials These methods have shown good agreement with experiments for simple geometries for which the analytical calculation of the effective properties is possible. This article (i) explores a more complex geometric variant of the metamaterial proposed by Dupont et al. to reduce its resonant frequencies, (ii) proposes a hybrid numerical-analytical modeling method to consider more precisely the thermoviscous losses in metamaterials, and

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