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  • Letter
  • Open Access

Phononic supercrystal as a highly absorbing metamaterial

Martin Ibarias* and José Sánchez-Dehesa†

Arkadii Krokhin‡

  • *Contact author: maibaal1@eln.upv.es
  • †Contact author: jsdehesa@upv.es
  • ‡Contact author: arkady@unt.edu
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Phys. Rev. Research 6, L042005 – Published 4 October, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L042005

Abstract

We demonstrate analytically, numerically, and experimentally that a 2D supercrystal (SC)—an elastic structure of solid rods with two distinct spatial periods embedded in a viscous fluid—exhibits very high acoustic absorption. Smaller diameter rods arranged in a 2D lattice with a smaller period serve as an effective medium with high viscosity for a set of larger rods arranged in a lattice of much larger period. The enhancement of acoustic absorption is due to strong viscous friction within a narrow layer with high gradients of velocity formed around each scatterer. The SC as a whole is considered in the homogenization limit of frequencies where it behaves as a metafluid with an effective speed of sound and effective viscosity. Analytical results for the effective parameters are calculated for any Bravais lattices and arbitrary cross-sections of the rods. Experimental measurements of acoustic absorption in a supercrystal with hexagonal lattices for both types of rods are in a good agreement with analytical and numerical results.

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References (31)

  1. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Elsevier, Oxford, 1984).
  2. M. I. Hussein and M. J. Frazier, Metadamping: An emergent phenomenon in dissipative metamaterials, J. Sound Vib. 332, 4767 (2013).
  3. C. Lagarrigue, J. P. Groby, V. Tournat, O. Dazel, and O. Umnova, Absorption of sound by porous layers with embedded periodic arrays of resonant inclusions, J. Acoust. Soc. Am. 134, 4670 (2013).
  4. D. M. Garza-Agudelo, V. Cutanda Henriquez, C.-H. Jeong, and P. R. Andersen, Characterization and optimization of the angle dependent acoustic absorption of 2D infinite periodic surfaces of Helmholtz resonators, J. Theor. Comp. Acout. 31, 2250010 (2023).
  5. X. H. Zhang and Z. G. Qu, Viscous and thermal dissipation during the sound propagation in the continuously graded phononic crystals, Appl. Acoustics 189, 108606 (2022).
  6. S. Wang, B. Hu, and Y. Du, Sound absorption of periodically cavities with gradient changes of radii and distances between cavities in a soft elastic medium, Appl. Acoustics 170, 107501 (2020).
  7. X. H. Zhang, Z. Qu, and H. Wang, Engineering acoustic metamaterials for sound absorption: From uniform to gradient structures, iScience 23, 101110 (2020).
  8. V. Romero-García, N. Jiménez, J.-P. Groby, A. Merkel, V. Tournat, G. Theocharis, O. Richoux, and V. Pagneux, Perfect absorption in mirror-symmetric acoustic metascreens, Phys. Rev. Appl. 14, 054055 (2020).
  9. S. Huang, Z. Zhou, D. Li, T. Liu, X. Wang, J. Zhu, and Y. Li, Compact broadband acoustic sink with coherently coupled weak resonances, Sci. Bull. 65, 373 (2020).
  10. J.-P. Groby, A. Wirgin, L. De Ryck, W. Lauriks, R. P. Gilbert, and Y. S. Xu, Acoustic response of a rigid-frame porous medium plate with a periodic set of inclusions, J. Acoust. Soc. Am. 126, 685 (2009); J.-P. Groby, O. Dazel, A. Duclos, L. Boeckx, and L. Kelders, Enhancing the absorption coefficient of a backed rigid frame porous layer by embedding circular periodic inclusions, ibid. 130, 3771 (2011).
  11. C. R. Liu, J. H. Wu, Z. Yang, and F. Ma, Ultra-broadband acoustic absorption of a thin microperforated panel metamaterial with multi-order resonance, Compos. Struct. 246, 112366 (2020).
  12. X. Li, B. Liu, and Q. Wu, Enhanced low-frequency sound absorption of a porous layer mosaicked with perforated resonator, Polymers 14, 223 (2022).
  13. A. Climente, D. Torrent, and J. Sánchez-Dehesa, Omnidirectional broadband acoustic absorber based on metamaterials, Appl. Phys. Lett. 100, 144103 (2012); V. C. Henríquez, and J. Sánchez-Dehesa, Viscothermal effects in a two-dimensional acoustic black hole: A boundary element approach, Phys. Rev. Appl. 15, 064057 (2021).
  14. Y. A. Godin, Effective complex permittivity tensor of a periodic array of cylinders, J. Math. Phys. 54, 053505 (2013).
  15. M. D. Guild, V. M. Garcia-Chocano, W. Kan, and J. Sánchez-Dehesa, Enhanced inertia from lossy effective fluids using multi-scale sonic crystals, AIP Adv. 4, 124302 (2014).
  16. M. D. Guild, V. M. Garcia-Chocano, W. Kan, and J. Sánchez-Dehesa, Acoustic metamaterial absorbers based on multilayered sonic crystals, J. Appl. Phys. 117, 114902 (2015).
  17. M. Ibarias, Y. Zubov, J. Arriaga, and A. A. Krokhin, Phononic crystal as a homogeneous viscous metamaterial, Phys. Rev. Res. 2, 022053(R) (2020).
  18. M. Ibarias, J. Doporto, A. A. Krokhin, and J. Arriaga, Tuning the decay of sound in a viscous metamaterial, Phil. Trans. R. Soc. A. 380, 20220007 (2022).
  19. D. Shymkiv and A. Krokhin, Effects of viscous dissipation in propagation of sound in periodic layered structures, J. Acoust. Soc. Am. 155, 990 (2024).
  20. C.-Y. Lee, M. J. Leamy, and J. H. Nadler, Frequency band structure and absorption predictions for multi-periodic acoustic composites, J. Sound Vib. 329, 1809 (2010).
  21. E. E. Narimanov, Photonic hypercrystals, Phys. Rev. X 4, 041014 (2014).
  22. Q. Yao, L. Liu, S. Malola et al., Supercrystal engineering of atomically precise gold nanoparticles promoted by surface dynamics, Nat. Chem. 15, 230 (2023).
  23. K. Aryana and M. B. Zanjani, Diamond family of colloidal supercrystals as phononic metamaterials, J. Appl. Phys. 123, 185103 (2018).
  24. A. A. Krokhin, J. Arriaga, and L. N. Gumen, Speed of sound in periodic elastic composites, Phys. Rev. Lett. 91, 264302 (2003).
  25. D. Torrent, A. Håkansson, F. Cervera, and J. Sánchez-Dehesa, Homogenization of 2D clusters of rigid rods in air, Phys. Rev. Lett. 96, 204302 (2006).
  26. Y. Wu, Y. Lai, and Z.-Q. Zhang, Effective medium theory for elastic metamaterials in two dimensions, Phys. Rev. B 76, 205313 (2007).
  27. See Supplementary Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L042005 for the details of calculations of the effective parameters (speed of sound and decay coefficient) for 2D phononic crystal.
  28. D. Torrent and J. Sánchez-Dehesa, Anisotropic mass density by 2D acoustic metmaterials, New J. Phys. 10, 023004 (2008); L. N. Gumen, J. Arriaga, and A. A. Krokhin, Metafluid with anisotropic dynamic mass, Low Temp. Phys. 37, 975 (2011).
  29. M. J. Cops, J. G. McDaniel, E. A. Maglius, D. J. Bamford, and M. Berggren, Estimates of acoustic absorption in porous materials based on viscous boundary layers modeles as boundary conditions, J. Acoust. Soc. Am. 148, 1624 (2020).
  30. B. H. Song and J. S. Bolton, A transfer-matrix approach for estimating the characteristic impedance and wave numbers of limp and rigid porous materials, J. Acoust. Soc. Am. 107, 1131 (2000).
  31. J. E. Avron, Odd viscosity, J. Stat. Phys. 92, 543 (1998); X. M. de Wit, M. Fruchart, T. Khain, F. Toschi, and V. Vitelli, Pattern formation by turbulent cascades, Nature (London) 627, 515 (2024).

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Phys. Rev. Research 6, L042005– Published 4 October, 2024
  • Received 3 April 2024
  • Accepted 19 September 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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