Design of acoustic metamaterials made of Helmholtz resonators for perfect absorption by using the complex frequency plane

V. Romero-García; N. Jiménez; G. Theocharis; V. Achilleos; A. Merkel; O. Richoux; V. Tournat; J.-P. Groby; V. Pagneux

doi:10.5802/crphys.32

Design of acoustic metamaterials made of Helmholtz resonators for perfect absorption by using the complex frequency plane
[Conception de métamatériaux acoustiques constitués de résonateurs de Helmholtz pour l’absorption parfaite dans le plan des fréquences complexes]

V. Romero-García ¹ ; N. Jiménez ¹ ; G. Theocharis ¹ ; V. Achilleos ¹ ; A. Merkel ¹ ; O. Richoux ¹ ; V. Tournat ¹ ; J.-P. Groby ¹ ; V. Pagneux ¹

¹ Laboratoire d’Acoustique de l’Université du Mans (LAUM), UMR 6613, Institut d’Acoustique - Graduate School (IA-GS), CNRS, Le Mans Université, France

Comptes Rendus. Physique, Metamaterials 2, Volume 21 (2020) no. 7-8, pp. 713-749.

Résumé
Abstract

Dans cette revue, nous présentons des résultats sur l’absorption acoustique parfaite sub-longueur d’onde faisant appel à des métamatériaux acoustiques avec des résonateurs Helmholtz pour différentes configurations. L’absorption parfaite à basse fréquence nécessite une augmentation du nombre d’états aux basses fréquences ainsi que de trouver les bonnes conditions pour une adaptation d’impédance avec le milieu environnant. Si en outre, on souhaite réduire les dimensions géométriques des structures proposées pour des questions pratiques, on peut utiliser des résonateurs locaux judicieusement conçus afin d’attendre une absorption parfaite sub-longueur d’onde. Les résonateurs de Helmholtz se sont révélés de bons candidats en raison de leur accordabilité aisée de la géométrie, donc de la fréquence de résonance, de la fuite d’énergie et des pertes intrinsèques. Lorsqu’ils sont branchés à un guide d’ondes ou à un milieu environnant, ils se comportent comme des systèmes ouverts, avec pertes et résonances caractérisés par leur fuite d’énergie et leurs pertes intrinsèques. L’équilibre entre ces deux aspects représente la condition de couplage critique et donne lieu à un maximum d’absorption d’énergie. Le mécanisme de couplage critique est ici représenté dans le plan de fréquence complexe afin d’interpréter la condition d’adaptation d’impédance. Dans cette revue, nous discutons en détail la possibilité d’obtenir une absorption parfaite par ces conditions de couplage critiques dans différents systèmes tels que la réflexion (à un port), la transmission (à deux ports) ou les systèmes à trois ports.

In this review, we present the results on sub-wavelength perfect acoustic absorption using acoustic metamaterials made of Helmholtz resonators with different setups. Low frequency perfect absorption requires to increase the number of states at low frequencies and finding the good conditions for impedance matching with the background medium. If, in addition, one wishes to reduce the geometric dimensions of the proposed structures for practical issues, one can use properly designed local resonators and achieve sub-wavelength perfect absorption. Helmholtz resonators have been shown good candidates due to their easy tunability of the geometry, so of the resonance frequency, the energy leakage and the intrinsic losses. When plugged to a waveguide or a surrounding medium they behave as open, lossy and resonant systems characterized by their energy leakage and intrinsic losses. The balance between these two represents the critical coupling condition and gives rise to maximum energy absorption. The critical coupling mechanism is represented here in the complex frequency plane in order to interpret the impedance matching condition. In this review we discuss in detail the possibility to obtain perfect absorption by these critical coupling conditions in different systems such as reflection (one-port), transmission (two-ports) or three-ports systems.

Publié le : 2021-01-19

DOI : 10.5802/crphys.32

Keywords: Acoustic metamaterials, Perfect absorption, Helmholtz resonators, Locally resonant materials, Critical coupling, Complex frequency plane
Mots-clés : Métamatériaux acoustiques, Absorption parfaite, Résonateurs de Helmholtz, Résonateurs locaux, Couplage critique, Plan des fréquences complexes

Affiliations des auteurs :

V. Romero-García ¹ ; N. Jiménez ¹ ; G. Theocharis ¹ ; V. Achilleos ¹ ; A. Merkel ¹ ; O. Richoux ¹ ; V. Tournat ¹ ; J.-P. Groby ¹ ; V. Pagneux ¹

¹ Laboratoire d’Acoustique de l’Université du Mans (LAUM), UMR 6613, Institut d’Acoustique - Graduate School (IA-GS), CNRS, Le Mans Université, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Design of acoustic metamaterials made of {Helmholtz} resonators for perfect absorption by using the complex frequency plane},
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V. Romero-García; N. Jiménez; G. Theocharis; V. Achilleos; A. Merkel; O. Richoux; V. Tournat; J.-P. Groby; V. Pagneux. Design of acoustic metamaterials made of Helmholtz resonators for perfect absorption by using the complex frequency plane. Comptes Rendus. Physique, Metamaterials 2, Volume 21 (2020) no. 7-8, pp. 713-749. doi : 10.5802/crphys.32. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.32/

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Joshua Morris; Weidi Wang; Darshil Shah; Thomas Plaisted; Christopher J. Hansen; Alireza V. Amirkhizi Expanding the design space and optimizing stop bands for mechanical metamaterials, Materials Design, Volume 216 (2022), p. 110510 | DOI:10.1016/j.matdes.2022.110510
Baozhu Cheng; Xinyu Guo; Nansha Gao; Hong Hou Realizing the perfect sound absorption and broadening effective band using porous material and micro-perforated plate, Modern Physics Letters B, Volume 36 (2022) no. 26n27 | DOI:10.1142/s0217984922501445
M. Malléjac; P. Sheng; V. Tournat; V. Romero-García; J.-P. Groby Slow-Sound-Based Delay-Line Acoustic Metamaterial, Physical Review Applied, Volume 17 (2022) no. 4 | DOI:10.1103/physrevapplied.17.044035
Sichao Qu; Ping Sheng Microwave and Acoustic Absorption Metamaterials, Physical Review Applied, Volume 17 (2022) no. 4 | DOI:10.1103/physrevapplied.17.047001
Nan Gao; Zhen Dong; Ho Yiu Mak; Ping Sheng Manipulation of Low-Frequency Sound with a Tunable Active Metamaterial Panel, Physical Review Applied, Volume 17 (2022) no. 4 | DOI:10.1103/physrevapplied.17.044037
Yang Meng; Vicente Romero-García; Gwénaël Gabard; Jean-Philippe Groby; Charlie Bricault; Sébastien Goudé; Ping Sheng Fundamental constraints on broadband passive acoustic treatments in unidimensional scattering problems, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 478 (2022) no. 2265 | DOI:10.1098/rspa.2022.0287
Leo-Paul Euvé; Kim Pham; Philippe Petitjeans; Vincent Pagneux; Agnès Maurel Time domain modelling of a Helmholtz resonator analogue for water waves, Journal of Fluid Mechanics, Volume 920 (2021) | DOI:10.1017/jfm.2021.450
Ho Yiu Mak; Xiaonan Zhang; Zhen Dong; Susumu Miura; Takuro Iwata; Ping Sheng Going Beyond the Causal Limit in Acoustic Absorption, Physical Review Applied, Volume 16 (2021) no. 4 | DOI:10.1103/physrevapplied.16.044062

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