# A Flexible Meta-Curtain for Simultaneous Soundproofing and Ventilation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design of Flexible Meta-Curtain

#### 2.1. Geometry Design

#### 2.2. Band Structure and Eigenstate Analysis

#### 2.3. Sound Transmission Loss Analysis

## 3. Fabrication and Experimental Measurement of Flexible Meta-Curtain

#### 3.1. Fabricated Unit Cell and Measurement of Sound Transmission Loss

#### 3.2. Fabricated Full-Size Meta-Curtain and Measurement of Sound Transmission Loss

## 4. Tunability on Geometrical Parameters

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Kang, J.; Brocklesby, M.W. Feasibility of applying micro-perforated absorbers in acoustic window systems. Appl. Acoust.
**2005**, 66, 669–689. [Google Scholar] [CrossRef] - Ma, G.; Sheng, P. Acoustic metamaterials: From local resonances to broad horizons. Sci. Adv.
**2016**, 2, e1501595. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Assouar, B.; Liang, B.; Wu, Y.; Li, Y.; Cheng, J.C.; Jing, Y. Acoustic metasurfaces. Nat. Rev. Mater.
**2018**, 3, 460–472. [Google Scholar] [CrossRef] [Green Version] - Zhang, S.; Xia, C.; Fang, N. Broadband acoustic cloak for ultrasound waves. Phys. Rev. Lett.
**2011**, 106, 024301. [Google Scholar] [CrossRef] - Sanchis, L.; García-Chocano, V.M.; Llopis-Pontiveros, R.; Climente, A.; Martínez-Pastor, J.; Cervera, F.; Sánchez-Dehesa, J. Three-dimensional axisymmetric cloak based on the cancellation of acoustic scattering from a sphere. Phys. Rev. Lett.
**2013**, 110, 124301. [Google Scholar] [CrossRef] - Zigoneanu, L.; Popa, B.I.; Cummer, S.A. Three-dimensional broadband omnidirectional acoustic ground cloak. Nat. Mater.
**2014**, 13, 352–355. [Google Scholar] [CrossRef] [Green Version] - Zhang, X.; Xiao, M.; Cheng, Y.; Lu, M.H.; Christensen, J. Topological sound. Commun. Phys.
**2018**, 1, 97. [Google Scholar] [CrossRef] [Green Version] - Ma, G.; Xiao, M.; Chan, C.T. Topological phases in acoustic and mechanical systems. Nat. Rev. Phys.
**2019**, 1, 281–294. [Google Scholar] [CrossRef] - Xue, H.; Yang, Y.; Zhang, B. Topological acoustics. Nat. Rev. Mater.
**2022**, 1, 17. [Google Scholar] [CrossRef] - Qu, S.; Gao, N.; Tinel, A.; Morvan, B.; Groby, P.; Sheng, P.; Bay, W.; Kong, H. Underwater metamaterial absorber with impedance-matched composite. Sci. Adv.
**2022**, 8, eabm4206. [Google Scholar] [CrossRef] - Kim, S.H.; Lee, S.H. Air transparent soundproof window. AIP Adv.
**2014**, 4, 117123. [Google Scholar] [CrossRef] - Kurdi, M.H.; Duncan, G.S.; Nudehi, S.S. Optimal design of a helmholtz resonator with a flexible end plate. J. Vib. Acoust.
**2014**, 136, 031004. [Google Scholar] [CrossRef] - Cheng, Y.; Zhou, C.; Yuan, B.G.; Wu, D.J.; Wei, Q.; Liu, X.J. Ultra-sparse metasurface for high reflection of low-frequency sound based on artificial Mie resonances. Nat. Mater.
**2015**, 14, 1013–1019. [Google Scholar] [CrossRef] [PubMed] - Jiménez, N.; Romero-García, V.; Pagneux, V.; Groby, J.P. Quasiperfect absorption by subwavelength acoustic panels in transmission using accumulation of resonances due to slow sound. Phys. Rev. B
**2017**, 95, 014205. [Google Scholar] [CrossRef] [Green Version] - Jung, J.W.; Kim, J.E.; Lee, J.W. Acoustic metamaterial panel for both fluid passage and broadband soundproofing in the audible frequency range. Appl. Phys. Lett.
**2018**, 112, 041903. [Google Scholar] [CrossRef] - Wu, X.; Au-Yeung, K.Y.; Li, X.; Roberts, R.C.; Tian, J.; Hu, C.; Huang, Y.; Wang, S.; Yang, Z.; Wen, W. High-efficiency ventilated metamaterial absorber at low frequency. Appl. Phys. Lett.
**2018**, 112, 103505. [Google Scholar] [CrossRef] [Green Version] - Yang, J.; Lee, J.S.; Lee, H.R.; Kang, Y.J.; Kim, Y.Y. Slow-wave metamaterial open panels for efficient reduction of low-frequency sound transmission. Appl. Phys. Lett.
**2018**, 112, 091901. [Google Scholar] [CrossRef] - Li, L.J.; Zheng, B.; Zhong, L.M.; Yang, J.; Liang, B.; Cheng, J.C. Broadband compact acoustic absorber with high-efficiency ventilation performance. Appl. Phys. Lett.
**2018**, 113, 103501. [Google Scholar] [CrossRef] - Lee, T.; Nomura, T.; Dede, E.M.; Iizuka, H. Ultrasparse Acoustic Absorbers Enabling Fluid Flow and Visible-Light Controls. Phys. Rev. Appl.
**2019**, 11, 024022. [Google Scholar] [CrossRef] - Lee, T.; Nomura, T.; Iizuka, H. Damped resonance for broadband acoustic absorption in one-port and two-port systems. Sci. Rep.
**2019**, 9, 13077. [Google Scholar] [CrossRef] - Su, X.; Banerjee, D. Extraordinary sound isolation using an ultrasparse array of degenerate anisotropic scatterers. Phys. Rev. Appl.
**2020**, 13, 064047. [Google Scholar] [CrossRef] - Kim, D.-Y.; Ih, J.-G. Wideband reduction of in-duct noise using acoustic metamaterial with serially connected resonators made. Appl. Phys. Lett.
**2020**, 116, 251904. [Google Scholar] [CrossRef] - Nguyen, H.; Wu, Q.; Xu, X.; Chen, H.; Tracy, S.; Huang, G. Broadband acoustic silencer with ventilation based on slit-type Helmholtz resonators. Appl. Phys. Lett.
**2020**, 117, 134103. [Google Scholar] [CrossRef] - Kumar, S.; Xiang, T.B.; Lee, H.P. Ventilated acoustic metamaterial window panels for simultaneous noise shielding and air circulation. Appl. Acoust.
**2020**, 159, 107088. [Google Scholar] [CrossRef] - Melnikov, A.; Maeder, M.; Friedrich, N.; Pozhanka, Y.; Wollmann, A.; Scheffler, M.; Oberst, S.; Powell, D.; Marburg, S. Acoustic metamaterial capsule for reduction of stage machinery noise. J. Acoust. Soc. Am.
**2020**, 147, 1491–1503. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Dong, R.; Mao, D.; Wang, X.; Li, Y. Ultrabroadband Acoustic Ventilation Barriers via Hybrid-Functional Metasurfaces. Phys. Rev. Appl.
**2021**, 15, 024044. [Google Scholar] [CrossRef] - Liu, C.; Shi, J.; Zhao, W.; Zhou, X.; Ma, C.; Peng, R.; Wang, M.; Hang, Z.H.; Liu, X.; Christensen, J.; et al. Three-Dimensional Soundproof Acoustic Metacage. Phys. Rev. Lett.
**2021**, 127, 084301. [Google Scholar] [CrossRef] - Fusaro, G.; Yu, X.; Lu, Z.; Cui, F.; Kang, J. A metawindow with optimised acoustic and ventilation performance. Appl. Sci.
**2021**, 11, 3168. [Google Scholar] [CrossRef] - Shen, L.; Zhu, Y.; Mao, F.; Gao, S.; Su, Z.; Luo, Z.; Zhang, H.; Assouar, B. Broadband Low-Frequency Acoustic Metamuffler. Phys. Rev. Appl.
**2021**, 16, 064057. [Google Scholar] [CrossRef] - Xiang, X.; Tian, H.; Huang, Y.; Wu, X.; Wen, W. Manually tunable ventilated metamaterial absorbers. Appl. Phys. Lett.
**2021**, 118, 053504. [Google Scholar] [CrossRef] - Liu, C.; Wang, H.; Liang, B.; Cheng, J.; Lai, Y. Low-frequency and broadband muffler via cascaded labyrinthine metasurfaces. Appl. Phys. Lett.
**2022**, 120, 231702. [Google Scholar] [CrossRef] - Ma, G.; Yang, M.; Yang, Z.; Sheng, P. Low-frequency narrow-band acoustic filter with large orifice. Appl. Phys. Lett.
**2013**, 103, 011903. [Google Scholar] [CrossRef] [Green Version] - Zhang, H.L.; Zhu, Y.F.; Liang, B.; Yang, J.; Yang, J.; Cheng, J.C. Omnidirectional ventilated acoustic barrier. Appl. Phys. Lett.
**2017**, 111, 203502. [Google Scholar] [CrossRef] [Green Version] - Wang, X.; Luo, X.; Yang, B.; Huang, Z. Ultrathin and durable open metamaterials for simultaneous ventilation and sound reduction. Appl. Phys. Lett.
**2019**, 115, 171902. [Google Scholar] [CrossRef] - Ghaffarivardavagh, R.; Nikolajczyk, J.; Anderson, S.; Zhang, X. Ultra-open acoustic metamaterial silencer based on Fano-like interference. Phys. Rev. B
**2019**, 99, 024302. [Google Scholar] [CrossRef] - Sun, M.; Fang, X.; Mao, D.; Wang, X.; Li, Y. Broadband Acoustic Ventilation Barriers. Phys. Rev. Appl.
**2020**, 13, 044028. [Google Scholar] [CrossRef] - Shi, J.; Liu, C.; Liu, X.; Lai, Y. Ventilative meta-window with broadband low-frequency acoustic insulation. J. Appl. Phys.
**2021**, 129, 094901. [Google Scholar] [CrossRef] - Nguyen, H.Q.; Wu, Q.; Chen, H.; Chen, J.J.; Yu, Y.K.; Tracy, S.; Huang, G.L. A Fano-based acoustic metamaterial for ultra-broadband sound barriers. Proc. R. Soc. A
**2021**, 477, 20210024. [Google Scholar] [CrossRef] - Xu, Z.X.; Zheng, B.; Yang, J.; Liang, B.; Cheng, J.C. Machine-Learning-Assisted Acoustic Consecutive Fano Resonances: Application to a Tunable Broadband Low-Frequency Metasilencer. Phys. Rev. Appl.
**2021**, 16, 044020. [Google Scholar] [CrossRef] - García-Chocano, V.M.; Cabrera, S.; Sánchez-Dehesa, J. Broadband sound absorption by lattices of microperforated cylindrical shells. Appl. Phys. Lett.
**2012**, 101, 184101. [Google Scholar] [CrossRef] - Xu, Z.; Gao, H.; Ding, Y.; Yang, J.; Liang, B.; Cheng, J. Topology-Optimized Omnidirectional Broadband Acoustic Ventilation Barrier. Phys. Rev. Appl.
**2020**, 10, 054016. [Google Scholar] [CrossRef] - Zhang, H.L.; Zhu, Y.F.; Liang, B.; Yang, J.; Yang, J.; Cheng, J.C. Sound Insulation in a Hollow Pipe with Subwavelength Thickness. Sci. Rep.
**2017**, 7, 44106. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Shen, C.; Xie, Y.; Li, J.; Cummer, S.A.; Jing, Y. Acoustic metacages for sound shielding with steady air flow. J. Appl. Phys.
**2018**, 123, 124501. [Google Scholar] [CrossRef] - Ge, Y.; Sun, H.X.; Yuan, S.Q.; Lai, Y. Switchable omnidirectional acoustic insulation through open window structures with ultrathin metasurfaces. Phys. Rev. Mater.
**2019**, 3, 065203. [Google Scholar] [CrossRef] - Kumar, S.; Lee, H.P. Recent advances in acoustic metamaterials for simultaneous sound attenuation and air ventilation performances. Crystals
**2020**, 10, 686. [Google Scholar] [CrossRef] - Dong, R.; Sun, M.; Mo, F.; Mao, D.; Wang, X.; Li, Y. Recent advances in acoustic ventilation barriers. J. Phys. D. Appl. Phys.
**2021**, 54, 403002. [Google Scholar] [CrossRef] - Lee, H.P.; Kumar, S. Perspectives on the Sonic Environment and Noise Mitigations during the COVID-19 Pandemic Era. Acoustics
**2021**, 3, 493–506. [Google Scholar] [CrossRef] - Fang, N.; Xi, D.; Xu, J.; Ambati, M.; Srituravanich, W.; Sun, C.; Zhang, X. Ultrasonic metamaterials with negative modulus. Nat. Mater.
**2006**, 5, 452–456. [Google Scholar] [CrossRef] - Roger, W. Pryor Multiphysics Modeling Using COMSOL: A First Principles Approach; Jones & Bartlett Learning: Sudbury, MA, Canada, 2011. [Google Scholar]
- Indaleeb, M.M.; Banerjee, S.; Ahmed, H.; Saadatzi, M.; Ahmed, R. Deaf band based engineered Dirac cone in a periodic acoustic metamaterial: A numerical and experimental study. Phys. Rev. B
**2019**, 99, 024311. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Schematic diagram of the flexible meta-curtain, which is composed of two cascaded films separated by a certain distance. Circular holes are periodically distributed on the films for ventilation. (

**b**) Front and side views of a curved unit cell. (

**c**) Band structure of the meta-curtain with a flat shape. Eigenstates at the Z point (marked by red and orange stars in (

**c**)) for (

**d**) the flat unit cell and (

**e**) the curved unit cell. (

**f**) Sound transmission loss (STL) spectra for the flat and curved meta-curtains.

**Figure 2.**(

**a**) Photograph of a meta-unit of the meta-curtain. (

**b**) Photograph and (

**c**) diagram of the experimental platform of the one-dimensional acoustic waveguide. (

**d**) Measured and (

**e**) simulated STL spectra for the meta-unit and the contrast. (

**f**) Simulated acoustic pressure field distribution for the meta-unit located at the STL peak of 1350 Hz.

**Figure 3.**(

**a**) Photograph and (

**b**) diagram of the three-dimensional experimental setup. (

**c**) Measured and simulated STL spectra for a flat meta-curtain with $\overline{K}=0$. (

**d**) Measured STL spectra for a curved meta-curtain with $\overline{K}=1.2$. (

**e**) Photograph of a square-shaped pipe tightly sealed by the flexible meta-curtain. (

**f**) Measured STL spectra for the case of (

**e**).

**Figure 4.**Simulated STL spectra as a function of (

**a**) the thickness of the film, (

**b**) the height of the air cavity, (

**c**) the diameter of the central hole, and (

**d**) the lattice constant of the meta-unit.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Cui, X.; Liu, C.; Shi, J.; Shen, C.; Liu, X.; Lai, Y.
A Flexible Meta-Curtain for Simultaneous Soundproofing and Ventilation. *Symmetry* **2022**, *14*, 2348.
https://doi.org/10.3390/sym14112348

**AMA Style**

Cui X, Liu C, Shi J, Shen C, Liu X, Lai Y.
A Flexible Meta-Curtain for Simultaneous Soundproofing and Ventilation. *Symmetry*. 2022; 14(11):2348.
https://doi.org/10.3390/sym14112348

**Chicago/Turabian Style**

Cui, Xiaobin, Chenkai Liu, Jinjie Shi, Changhui Shen, Xiaozhou Liu, and Yun Lai.
2022. "A Flexible Meta-Curtain for Simultaneous Soundproofing and Ventilation" *Symmetry* 14, no. 11: 2348.
https://doi.org/10.3390/sym14112348