The acoustical design and modelling of a subwavelength hexagonal acoustic metamaterial for multipurpose use and potential building applications1

Journal title RIVISTA ITALIANA DI ACUSTICA
Author/s Denilson Ramosa, Francesco Pompoli, Luís Godinho, Paulo Amado-Mendes, Paulo Mareze
Online First 5/8/2026 Issue 2026/Online First
Language English Pages 14 P. 1-14 File size 2939 KB
DOI 10.3280/ria2026oa22128
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The development and application of noise control strategies on subwavelength regimes have thus demanded a continuous effort by several researchers. In recent decades, the advent of acoustic metamaterials arose as a novel strategy on the sound wave manipulation and the development of subwavelength dimensions acoustic devices. In previous works by the authors, analytical approaches were developed to provide a more comprehensive acoustic characterization of the proposed metamaterial through equivalent fluid models. In contrast, the present work aims to advance the concept by introducing the design of a ventilated subwavelength acoustic metamaterial and by examining its potential applicability across multiple building-related contexts, including sound absorption and sound transmission control. By means of optimized geometrical configurations, it is possible to achieve quasi-perfect sound absorption (α > 0.8[-]) or enhanced sound transmission loss efficiency (> 30 [dB]) within subwavelength regimes. The results demonstrate that the proposed acoustic metamaterial operates effectively at subwavelength dimensions and within selectively tuned attenuation frequency bands, enabling single-, dual-, triple-, or hexa-resonance configurations. These features introduce additional degrees of freedom into the overall design concept, offering promising applications across various engineering fields, particularly in building acoustics.

Keywords: acoustic metamaterial, association of Helmholtz resonators, sound absorption, sound transmission loss, building acoustics

  1. [16] Jiménez N, Romero-García V, Pagneux V, Groby JP. Rainbow-trapping absorbers: Broadband, perfect and asymmetric sound absorption by subwavelength panels for transmission problems. Sci Rep 2017;7:1–12. https://doi.org/10.1038/s41598-017-13706-4.
  2. [17] Jiménez N, Cox TJ, Vicent R, Groby J. Metadiffusers : Deep-subwavelength sound diffusers 2017. https://doi.org/10.1038/ s41598-017-05710-5.
  3. [18] Kumar S, Xiang TB, Lee HP. Ventilated acoustic metamaterial window panels for simultaneous noise shielding and air circulation. Applied Acoustics 2020;159:107088. https://doi. org/10.1016/j.apacoust.2019.107088.
  4. [19] Kim SH, Lee SH. Air transparent soundproof window. AIP Adv 2014;4. https://doi.org/10.1063/1.4902155.
  5. [20] Arjunan A, Baroutaji A, Robinson J, Vance A, Arafat A. Acoustic metamaterials for sound absorption and insulation in buildings. Build Environ 2024;251. https://doi.org/10.1016/j. buildenv.2024.111250.
  6. [21] Rubino C, Liuzzi S, Fusaro G, Martellotta F, Scrosati C, Garai M. Balancing ventilation and sound insulation in windows by means of metamaterials: A review of the state of the art. Build Environ 2025;275. https://doi.org/10.1016/j.buildenv.2025.112780.
  7. [22] Ramos D, Pompoli F, Marescotti C, Godinho L, Amado-Mendes P, Mareze P. Modelling the effective sound propagation properties of a hexagonal acoustic metamaterial using a dissipative equivalent-fluid approach under different termination conditions. J Sound Vib 2025;598. https://doi.org/10.1016/j. jsv.2024.118855.
  8. [23] Dell A, Krynkin A, Horoshenkov K V. The use of the transfer matrix method to predict the effective fluid properties of acoustical systems. Applied Acoustics 2021;182:108259. https://doi.org/10.1016/j.apacoust.2021.108259.
  9. [24] Jiménez N, Groby JP, Romero-García V. The Transfer Matrix Method in Acoustics: Modelling One-Dimensional Acoustic Systems, Phononic Crystals and Acoustic Metamaterials. vol.
  10. 143. Springer International Publishing; 2021. https://doi. org/10.1007/978-3-030-84300-7_4.
  11. [25] ISO. 10534-2:1998 Acoustics, Determination of sound absorption coefficient and impedance in impedance tubes — Part 2: Transfer-function method 1998;1998.
  12. [26] ASTM E2611. Standard Test Method for Measurement of Normal Incidence Sound Transmission of Acoustical Materials Based on the Transfer Matrix Method. ASTM International 2009:1–14. https://doi.org/10.1520/E2611-09.2.
  13. [27] Ramos D, Godinho L, Amado-Mendes P, Mareze P. Broadband low-frequency bidimensional honeycomb lattice metastructure based on the coupling of subwavelength resonators. Applied Acoustics 2022;199. https://doi.org/10.1016/j. apacoust.2022.109038.
  14. [28] Riccelli Del Teto Ramos D, Luís Manuel Cortesão Godinho P, Paulo Jorge Rodrigues Amado-Mendes P, Paulo Henrique Mareze
  15. P. STUDY AND DEVELOPMENT OF ACOUSTIC SOLUTIONS BASED ON ACOUSTIC METAMATERIAL CONCEPTS FOR THE CORRECTION OF VENTILATED ELEMENTS ON BUILDING FACADES. n.d.
  16. [29] Fusaro G, Barbaresi L, Cingolani M, Garai M, Ida E, Prato A, et al. Investigation of the impact of additive manufacturing techniques on the acoustic performance of a coiled-up resonator. J Acoust Soc Am 2023;153:2921. https://doi.org/10.1121/10.0019474.
  17. [30] Kuttruff H. Room Acoustics. CRC Press; 2002. https://doi. org/10.1201/9781482286632.
  18. [31] Barron M. The subjective effects of first reflections in concert halls—The need for lateral reflections. J Sound Vib 1971;15:475–94. https://doi.org/10.1016/0022-460X(71)90406-8.
  19. [1] Doak PE. Excitation, transmission and radiation of sound from source distributions in hard-walled ducts of finite length (II): The effects of duct length. J Sound Vib 1973;31:137–74. https://doi. org/10.1016/S0022-460X(73)80372-4.
  20. [2] Tijdeman H. On the propagation of sound waves in cylindrical tubes. J Sound Vib 1975;39:1–33. https://doi.org/10.1016/ S0022-460X(75)80206-9.
  21. [3] Zhang X, Qu Z, Wang H. iScience ll Engineering Acoustic Metamaterials for Sound Absorption : From Uniform to Gradient Structures. IScience 2020;23:101110. https://doi. org/10.1016/j.isci.2020.101110.
  22. [4] Kumar S, Lee HP. Recent Advances in Active Acoustic Metamaterials Recent Advances in Active Acoustic Metamaterials 2020. https://doi.org/10.1142/S1758825119500819.
  23. [5] Yu X, Lu Z, Liu T, Cheng L, Zhu J, Cui F. Sound transmission through a periodic acoustic metamaterial grating. J Sound Vib 2019;449:140–56. https://doi.org/10.1016/j.jsv.2019.02.042.
  24. [6] Akl W, Baz A. Active control of the dynamic density of acoustic metamaterials. Applied Acoustics 2021;178:108001. https://doi. org/10.1016/j.apacoust.2021.108001.
  25. [7] Liu Y, Xu W, Chen M, Yang T, Wang K, Huang X, et al. Three-dimensional fractal structure with double negative and density-near-zero properties on a subwavelength scale. Mater Des 2020;188:108470. https://doi.org/10.1016/j. matdes.2020.108470.
  26. [8] Cox T, D’Antonio P. Acoustic Absorbers and Diffusers. CRC Press; 2016. https://doi.org/10.1201/9781315369211.
  27. [9] Zielinski TG, Dauchez N, Boutin T, Leturia M, Wilkinson A, Chevillotte F, et al. Taking advantage of a 3D printing imperfection in the development of sound-absorbing materials.
  28. Applied Acoustics 2022;197. https://doi.org/10.1016/j. apacoust.2022.108941.
  29. [10] Zielinski TG, Chevillotte F, Deckers E. Sound absorption of plates with micro-slits backed with air cavities: Analytical estimations, numerical calculations and experimental validations. Applied Acoustics 2019;146:261–79. https://doi.org/10.1016/j. apacoust.2018.11.026.
  30. [11] Fang N, Xi D, Xu J, Ambati M, Srituravanich W, Sun C, et al. Ultrasonic metamaterials with negative modulus. Nat Mater 2006;5:452–6. https://doi.org/10.1038/nmat1644.
  31. [12] Cervenka M, Bednarík M. Optimized compact wideband reactive silencers with annular resonators. J Sound Vib 2020;484. https://doi.org/10.1016/j.jsv.2020.115497.
  32. [13] Lee SH, Park CM, Seo YM, Wang ZG, Kim CK. Acoustic metamaterial with negative modulus. Journal of Physics Condensed Matter 2009;21. https://doi.org/10.1088/0953-8984/21/17/175704.
  33. [14] Lan J, Li Y, Yu H, Li B, Liu X. Nonlinear effects in acoustic metamaterial based on a cylindrical pipe with ordered Helmholtz resonators. Phys Lett A 2017;381:1111–7. https://doi. org/10.1016/j.physleta.2017.01.036.
  34. [15] Jena DP, Dandsena J, Jayakumari VG. Demonstration of effective acoustic properties of different configurations of Helmholtz resonators. Applied Acoustics 2019;155:371–82. https://doi. org/10.1016/j.apacoust.2019.06.004.
  35. [32] Hou B, Wang L, Zeng Q, Mo J, Zhao W. Optimization strategies for enhancing speech intelligibility in underground platform public address systems. Build Environ 2025;280:113107. https://doi. org/10.1016/j.buildenv.2025.113107.
  36. [33] De Salis MHF, Oldham DJ, Sharples S. Noise control strategies for naturally ventilated buildings. Build Environ 2002;37:471–84. https://doi.org/10.1016/S0360-1323(01)00047-6.
  37. [34] Fusaro G, Kang J, Chang WS. Effective soundscape characterisation of an acoustic metamaterial based window: A comparison between laboratory and online methods. Applied Acoustics 2022;193. https://doi.org/10.1016/j. apacoust.2022.108754.
  38. [35] Böke J, Knaack U, Hemmerling M. State-of-the-art of intelligent building envelopes in the context of intelligent technical systems. Intelligent Buildings International 2019;11:27–45. https://doi.org/10.1080/17508975.2018.1447437.

Denilson Ramosa, Francesco Pompoli, Luís Godinho, Paulo Amado-Mendes, Paulo Mareze, The acoustical design and modelling of a subwavelength hexagonal acoustic metamaterial for multipurpose use and potential building applications1 in "RIVISTA ITALIANA DI ACUSTICA" Online First/2026, pp 1-14, DOI: 10.3280/ria2026oa22128