Optimization of a labyrinthine acoustic metamaterial for sound absorption in the frequency range 100–300 Hz
DOI:
https://doi.org/10.55753/aev.v35e52.36Keywords:
sound absorption, acoustic metamaterial, parametric optimizationAbstract
Controlling sound energy in closed environments over the entire frequency spectrum is an extremely important factor, especially when acoustic comfort is a necessity of the architectural design of the environment. This control is performed by acoustic treatment, the sound absorption coefficient being a physical parameter of the acoustic material used. However, conventional sound absorbing materials (e.g. foams and fibers) have geometric and operational limitations towards controlling the sound energy with respect to the low frequency region (100–600 Hz). Such control has recently gained notoriety with the advent of metamaterial absorbers (MMA). In this article we present a theoretical, numerical and experimental evaluation of an established low-frequency absorption metamaterial. The acoustic metamaterial is based on the theory of micro-perforated panels (MPP) and the concept of coiled-up spaces, which resemble a labyrinth. The effects of viscous friction and thermal diffusion, important in the analytical description of the model, are corroborated through a numerical analysis using the finite element method (FEM). The sound absorption coefficient of the metamaterial is maximized by a heuristic method for the 100–300 Hz frequency region. A sample of the metamaterial was manufactured using 3D printing technology and evaluated in an impedance tube apparatus. The results obtained reveal sound absorption of 0.97% at 216 Hz with relative bandwidth of 49.0%. This demonstrates that the acoustic metamaterial presents a subwavelength scale, since its total thickness is 0.026λ.
References
BA, Amadou; LAVIE, Antoine; LEBLANC, Alexandre. Soft 3d printed membrane type-acoustic metamaterials. In: Proceedings of the 23rd International Congress on Sound & Vibration. [S.l.: s.n.], 2016.
PENG, Hao; PAI, P Frank. Acoustic metamaterial plates for elastic wave absorption and structural vibration suppression. International Journal of Mechanical Sciences, Elsevier, v. 89, p. 350–361, 2014. doi: 10.1016/j.ijmecsci.2014.09.018. DOI: https://doi.org/10.1016/j.ijmecsci.2014.09.018
ALLARD, J-F; DAIGLE, Gilles. Propagation of sound in porous media: Modeling sound absorbing materials. Acoustical Society of America, 1994. doi: 10.1121/1.409801. DOI: https://doi.org/10.1121/1.409801
BIES, David H; HANSEN, Colin H; CAMPBELL, Richard H. Engineering noise control. [S.l.]: Acoustical Society of America, 1996. doi: 10.1121/1.416038. DOI: https://doi.org/10.1121/1.416038
WANG, Yang; ZHAO, Honggang; YANG, Haibin; ZHONG, Jie; ZHAO, Dan; LU, Zhongliang; WEN, Jihong. A tunable sound-absorbing metamaterial based on coiled-up space. Journal of Applied Physics, AIP Publishing LLC, v. 123, n. 18, p. 185109, 2018. doi: 10.1063/1.5026022. DOI: https://doi.org/10.1063/1.5026022
ZHAO, Honggang; WANG, Yang; WEN, Jihong; LAM, Yiu Wai; UMNOVA, Olga. A slim subwavelength absorber based on coupled microslits. Applied Acoustics, Elsevier, v. 142, p. 11–17, 2018. doi: 10.1016/j.apacoust.2018.08.004. DOI: https://doi.org/10.1016/j.apacoust.2018.08.004
ALMEIDA, Gildean N. Análise de um metamaterial acústico do tipo labiríntico na absorção sonora de baixas frequências. Dissertação (Mestrado) — Universidade Federal de Santa Catarina, Florianópolis, SC, 2019. DOI: https://doi.org/10.55753/aev.v35e52.36
MAA, Dah-You. Microperforated-panel wideband absorbers. Noise control engineering journal, v. 29, n. 3, p. 77–84, 1987. doi: 10.3397/1.2827694. DOI: https://doi.org/10.3397/1.2827694
WANG, Chunqi; HUANG, Lixi; ZHANG, Yumin. Oblique incidence sound absorption of parallel arrangement of multiple micro-perforated panel absorbers in a periodic pattern. Journal of Sound and Vibration, Elsevier, v. 333, n. 25, p. 6828–6842, 2014. doi: 10.1016/j.jsv.2014.08.009. DOI: https://doi.org/10.1016/j.jsv.2014.08.009
LI, Dengke; CHANG, Daoqing; LIU, Bilong. Enhanced low-to mid-frequency sound absorption using parallel-arranged perforated plates with extended tubes and porous material. Applied Acoustics, Elsevier, v. 127, p. 316–323, 2017. doi: 10.1016/j.apacoust.2017.06.019. DOI: https://doi.org/10.1016/j.apacoust.2017.06.019
BRAVO, Teresa; MAURY, Cédric; PINHÈDE, Cédric. Optimising the absorption and transmission properties of aircraft microperforated panels. Applied acoustics, Elsevier, v. 79, p. 47–57, 2014. Doi: 10.1016/j.apacoust.2013.12.009. DOI: https://doi.org/10.1016/j.apacoust.2013.12.009
COBO, Pedro; SIMÓN, Francisco. Multiple-layer microperforated panels as sound absorbers in buildings: A review. Buildings, Multidisciplinary Digital Publishing Institute, v. 9, n. 2, p. 53, 2019. Doi: 10.3390/buildings9020053. DOI: https://doi.org/10.3390/buildings9020053
MAREZE, Paulo H; BRANDÃO, Eric; FONSECA, William D’A; SILVA, Olavo M; LENZI, Arcanjo. Modeling of acoustic porous material absorber using rigid multiple micro-ducts network: Validation of the proposed model. Journal of Sound and Vibration, Elsevier, v. 443, p. 376–396, 2019. doi: 10.1016/j.jsv.2018.11.036. DOI: https://doi.org/10.1016/j.jsv.2018.11.036
BRANDÃO, Eric. Acústica de Salas: Projeto e Modelagem. 1. ed. São Paulo: Blucher, 2016. ISBN 9788521210061.
TANG, Yufan; XIN, Fengxian; HUANG, Lixi; LU, Tianjian. Deep subwavelength acoustic metamaterial for low-frequency sound absorption. EPL (Europhysics Letters), IOP Publishing, v. 118, n. 4, p. 44002, 2017. doi: 10.1209/0295-5075/118/44002. DOI: https://doi.org/10.1209/0295-5075/118/44002
JUNG, Jae Woong; KIM, Jae Eun; LEE, Jin Woo. Acoustic metamaterial panel for both fluid passage and broadband soundproofing in the audible frequency range. Applied Physics Letters, AIP Publishing LLC, v. 112, n. 4, p. 041903, 2018. doi: 10.1063/1.5004605. DOI: https://doi.org/10.1063/1.5004605
WU, Xiaoxiao; FU, Caixing; LI, Xin; MENG, Yan; GAO, Yibo; TIAN, Jingxuan; WANG, Li; HUANG, Yingzhou; YANG, Zhiyu; WEN, Weijia. Low-frequency tunable acoustic absorber based on split tube resonators. Applied Physics Letters, AIP Publishing LLC, v. 109, n. 4, p. 043501, 2016. doi: 10.1063/1.495995. DOI: https://doi.org/10.1063/1.4959959
LI, Junfei; WANG, Wenqi; XIE, Yangbo; POPA, Bogdan-Ioan; CUMMER, Steven A. A sound absorbing metasurface with coupled resonators. Applied Physics Letters, AIP Publishing LLC, v. 109, n. 9, p. 091908, 2016. doi: 10.1063/1.4961671. DOI: https://doi.org/10.1063/1.4961671
ZHAO, Xiang; CAI, Li; YU, Dianlong; LU, Zhimiao; WEN, Jihong. A low frequency acoustic insulator by using the acoustic metasurface to a helmholtz resonator. AIP Advances, AIP Publishing LLC, v. 7, n. 6, p. 065211, 2017. doi: 10.1063/1.4989819. DOI: https://doi.org/10.1063/1.4989819
KRUSHYNSKA, AO; BOSIA, F; MINIACI, M; PUGNO, NM. Spider web-structured labyrinthine acoustic metamaterials for low-frequency sound control. New Journal of Physics, IOP Publishing, v. 19, n. 10, p. 105001, 2017. doi: 10.1088/1367-2630/aa83f3. DOI: https://doi.org/10.1088/1367-2630/aa83f3
LEBLANC, Alexandre; LAVIE, Antoine. Three-dimensional-printed membrane-type acoustic metamaterial for low frequency sound attenuation. The Journal of the Acoustical Society of America, Acoustical Society of America, v. 141, n. 6, p. EL538–EL542, 2017. doi: 10.1121/1.4984623. DOI: https://doi.org/10.1121/1.4984623
DONDA, Krupali; ZHU, Yifan; FAN, Shi-Wang; CAO, Liyun; LI, Yong; ASSOUAR, Badreddine. Extreme low-frequency ultrathin acoustic absorbing metasurface. Applied Physics Letters, AIP Publishing LLC, v. 115, n. 17, p. 173506, 2019. doi: 10.1063/1.5122704. DOI: https://doi.org/10.1063/1.5122704
GAN, Woon Siong. New Acoustics Based on Metamaterials. [S.l.]: Springer, 2017. ISBN 9811063761. DOI: https://doi.org/10.1007/978-981-10-6376-3_11
ZWIKKER, Cornelis; KOSTEN, Cornelis Willem. Sound absorbing materials. [S.l.]: Elsevier, 1949.
GROBY, J-P; HUANG, W; LARDEAU, A; AURÉGAN, Y. The use of slow waves to design simple sound absorbing materials. Journal of Applied Physics, AIP Publishing LLC, v. 117, n. 12, p. 124903, 2015. doi: 10.1063/1.4915115. DOI: https://doi.org/10.1063/1.4915115
JIMÉNEZ, Noé; GROBY, Jean-Philippe; PAGNEUX, Vincent; ROMERO-GARCÍA, Vicent. Iridescent perfect absorption in critically-coupled acoustic metamaterials using the transfer matrix method. Applied Sciences, Multidisciplinary Digital Publishing Institute, v. 7, n. 6, p. 618, 2017. Doi: 10.3390/app7060618. DOI: https://doi.org/10.3390/app7060618
JIMÉNEZ, Noe; HUANG, Weichun; ROMERO-GARCÍA, Vicent; PAGNEUX, Vincent; GROBY, J-P. Ultra-thin metamaterial for perfect and quasi-omnidirectional sound absorption. Applied Physics Letters, AIP Publishing LLC, v. 109, n. 12, p. 121902, 2016. doi: 10.1063/1.4962328. DOI: https://doi.org/10.1063/1.4962328
ROMERO-GARCIA, Vicente; HLADKY-HENNION, Anne-Christine. Fundamentals and Applications of Acoustic Metamaterials: From Seismic to Radio Frequency. [S.l.]: John Wiley & Sons, 2019. ISBN 1786303361. DOI: https://doi.org/10.1002/9781119649182
ZHANG, Chi; HU, Xinhua. Three-dimensional single-port labyrinthine acoustic metamaterial: Perfect absorption with large bandwidth and tunability. Physical Review Applied, APS, v. 6, n. 6, p. 064025, 2016. doi: 10.1103/PhysRevApplied.6.064025. DOI: https://doi.org/10.1103/PhysRevApplied.6.064025
LI, Yong; ASSOUAR, Badreddine M. Acoustic metasurface-based perfect absorber with deep subwavelength thickness. Applied Physics Letters, AIP Publishing LLC, v. 108, n. 6, p. 063502, 2016. doi: 10.1063/1.4941338. DOI: https://doi.org/10.1063/1.4941338
WU, Fei; XIAO, Yong; YU, Dianlong; ZHAO, Honggang; WANG, Yang; WEN, Jihong. Low-frequency sound absorption of hybrid absorber based on micro-perforated panel and coiled-up channels. Applied Physics Letters, AIP Publishing LLC, v. 114, n. 15, p. 151901, 2019. Doi: 10.1063/1.5090355. DOI: https://doi.org/10.1063/1.5090355
LONG, Houyou; SHAO, Chen; LIU, Chen; CHENG, Ying; LIU, Xiaojun. Broadband near-perfect absorption of low-frequency sound by subwavelength metasurface. Applied Physics Letters, AIP Publishing LLC, v. 115, n. 10, p. 103503, 2019. doi: 10.1063/1.5109826. DOI: https://doi.org/10.1063/1.5109826
CHEN, Changru; DU, Zhibo; HU, Gengkai; YANG, Jun. A low-frequency sound absorbing material with subwavelength thickness. Applied Physics Letters, AIP Publishing LLC, v. 110, n. 22, p. 221903, 2017. doi: 10.1063/1.4984095. DOI: https://doi.org/10.1063/1.4984095
SHEN, Yuchen; YANG, Yanye; GUO, Xi-asheng; SHEN, Yong; ZHANG, Dong. Low-frequency anechoic metasurface based on coiled channel of gradient cross-section. Applied Physics Letters, AIP Publishing LLC, v. 114, n. 8, p. 083501, 2019. doi: 10.1063/1.5081926. DOI: https://doi.org/10.1063/1.5081926
WANG, Yang; ZHAO, Honggang; YANG, Haibin; ZHONG, Jie; WEN, Jihong. A space-coiled acoustic metamaterial with tunable low-frequency sound absorption. EPL (Europhysics Letters), IOP Publishing, v. 120, n. 5, p. 54001, 2018. doi: 10.1209/0295-5075/120/54001. DOI: https://doi.org/10.1209/0295-5075/120/54001
LI, Yong; LIANG, Bin; GU, Zhong-ming; ZOU, Xin-ye; CHENG, Jian-chun. Unidirectional acoustic transmission through a prism with near-zero refractive index. Applied Physics Letters, American Institute of Physics, v. 103, n. 5, p. 053505, 2013. doi: 10.1063/1.4817249. DOI: https://doi.org/10.1063/1.4817249
STINSON, Michael R. The propagation of plane sound waves in narrow and wide circular tubes, and generalization to uniform tubes of arbitrary cross-sectional shape. The Journal of the Acoustical Society of America, Acoustical Society of America, v. 89, n. 2, p. 550–558, 1991. Doi: 10.1121/1.400379. DOI: https://doi.org/10.1121/1.400379
MAREZE, Paulo Henrique. Análise da influência da microgeometria na absorção sonora de materiais porosos de estrutura rígida. Tese (Doutorado) — Universidade Federal de Santa Catarina, Florianópolis, SC, 2013. Disponível em: https://repositorio.ufsc.br/bitstream/handle/123456789/106792/320039.pdf?sequence=1&isAllowed=y
RYOO, Hyeonbin; JEON, Wonju. Dual-frequency sound-absorbing metasurface based on visco-thermal effects with frequency dependence. Journal of Applied Physics, AIP Publishing LLC, v. 123, n. 11, p. 115110, 2018. doi: 10.1063/1.5017540. DOI: https://doi.org/10.1063/1.5017540
MAA, Dah-You. Potential of microperforated panel absorber. The Journal of the Acoustical Society of America, Acoustical Society of America, v. 104, n. 5, p. 2861–2866, 1998. doi: 10.1121/1.423870. DOI: https://doi.org/10.1121/1.423870
RAYLEIGH, J.W.S. The Theory of Sound, 2. Aufl., Bd. 1-2. [S.l.]: London: MacMillan & Co, 1926.
CRANDALL, Irving Bardshar. Theory of vibrating systems and sound. [S.l.]: D. Van Nostrand Company, 1926.
INGARD, Uno. On the theory and design of acoustic resonators. The Journal of the acoustical society of America, Acoustical Society of America, v. 25, n. 6, p. 1037–1061, 1953. Doi: 10.1121/1.190723. DOI: https://doi.org/10.1121/1.1907235
MELLING, Thomas Henry. The acoustic impendance of perforates at medium and high sound pressure levels. Journal of Sound and Vibration, Elsevier, v. 29, n. 1, p. 1–65, 1973. doi: 10.1016/S0022-460X(73)80125-7. DOI: https://doi.org/10.1016/S0022-460X(73)80125-7
FOK, VA. Doklady akademii nauk. [S.l.]: SSSR, 1941.
RZHEVKIN, Serge ̆ı Nikolaevich. A course of lectures on the theory of sound. [S.l.]: Pergamon Press;[distributed in the Western Hemisphere by Macmillan, New York], 1963.
YANG, Min; SHENG, Ping. Sound absorption structures: From porous media to acoustic metamaterials. Annual Review of Materials Research, Annual Reviews, v. 47, p. 83–114, 2017. doi: 10.1146/annurev-matsci-070616-124032. DOI: https://doi.org/10.1146/annurev-matsci-070616-124032
TANG, Yufan; REN, Shuwei; MENG, Han; XIN, Fengxian; HUANG, Lixi; CHEN, Tianning; ZHANG, Chuanzeng; LU, Tian Jian. Hybrid acoustic metamaterial as super absorber for broadband low-frequency sound. Scientific reports, Nature Publishing Group, v. 7, p. 43340, 2017. Doi: 10.1038/srep43340. DOI: https://doi.org/10.1038/srep43340
WANG, Chunqi; HUANG, Lixi. On the acoustic properties of parallel arrangement of multiple micro-perforated panel absorbers with different cavity depths. The Journal of the Acoustical Society of America, Acoustical Society of America, v. 130, n. 1, p. 208–218, 2011. doi: 10.1121/1.3596459. DOI: https://doi.org/10.1121/1.3596459
MERKEL, A; THEOCHARIS, G; RICHOUX, Olivier; ROMERO-GARCÍA, Vicente; PAGNEUX, V. Control of acoustic absorption in one-dimensional scattering by resonant scatterers. Applied Physics Letters, AIP Publishing LLC, v. 107, n. 24, p. 244102, 2015. doi: 10.1063/1.4938121. DOI: https://doi.org/10.1063/1.4938121
STORN, Rainer; PRICE, Kenneth. Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. Journal of global optimization, Springer, v. 11, n. 4, p. 341–359, 1997. doi: 10.1023/A:1008202821328. DOI: https://doi.org/10.1023/A:1008202821328
VITALIY, Feoktistov. Differential evolution–in search of solutions. [S.l.]: Springer, New York, 2006. doi: 10.1007/978-0-387-36896-2. DOI: https://doi.org/10.1007/978-0-387-36896-2
GASPAR-CUNHA, António; TAKAHASHI, Ricardo; ANTUNES, Carlos Henggeler. Manual de computação evolutiva e metaheurística. [S.l.]: Imprensa da Universidade de Coimbra/Coimbra University Press, 2012. ISBN 9789892601502. DOI: https://doi.org/10.14195/978-989-26-0583-8
ORGANIZATION, International Standards. Acoustics—Determination of Sound Absorption Coefficient and Impedance in Impedance Tubes—Part 2: Transfer-Function Method. [S.l.]: International Standards Organization Geneva, Switzerland, 1998.
KANDLIKAR, Satish G; SCHMITT, Derek; CARRANO, Andres L; TAYLOR, James B. Characterization of surface roughness effects on pressure drop in single-phase flow in mini-channels. Physics of Fluids, American Institute of Physics, v. 17, n. 10, p. 100606, 2005. doi: 10.1063/1.1896985. DOI: https://doi.org/10.1063/1.1896985
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