Hilbert fractal acoustic metamaterials with negative mass density and bulk modulus on subwavelength scale

Man, Xianfeng; Luo, Zhen; Liu, Jian; Xia, Baizhan

doi:10.1016/j.matdes.2019.107911

Cited by 50 publications

(18 citation statements)

References 59 publications

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“…Further research could include extending the coastal-point calculations to the modified deposition models of sections VI and VII or for a magnetic version of the model which has been studied in [22]. In a more applied arena, optical and electromagnetic properties of the surface can be studied and tested in real-world applications such as the design of antennae [23] or acoustic metamaterials [24]. For these applications, it could be worthwhile to investigate the properties of the hierarchical random deposition model in different geometries, e.g., triangular, spherical, hexagonal etc., and with different boundary conditions.…”

Section: Discussionmentioning

confidence: 99%

Coastlines and percolation in a model for hierarchical random deposition

Berx

Bervoets

Giuraniuc

et al. 2021

Physica A: Statistical Mechanics and its Applications

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We revisit a known model in which (conducting) blocks are hierarchically and randomly deposited on a d-dimensional substrate according to a hyperbolic size law with the block size decreasing by a factor λ > 1 in each subsequent generation. In the first part of the paper the number of coastal points (in D = 1) or coastlines (in D = 2) is calculated, which are points or lines that separate a region at "sea level" and an elevated region. We find that this number possesses a non-universal character, implying a Euclidean geometry below a threshold value P c of the deposition probability P , and a fractal geometry above this value. Exactly at the threshold, the geometry is logarithmic fractal. The number of coastlines in D = 2 turns out to be exactly twice the number of coastal points in D = 1. We comment briefly on the surface morphology and derive a roughness exponent α. In the second part, we study the percolation probability for a current in this model and two extensions of it, in which both the scale factor and the deposition probability can take on different values between generations. We find that the percolation threshold P c is located at exactly the same value for the deposition probability as the threshold probability of the number of coastal points. This coincidence suggests that exactly at the onset of percolation for a conducting path, the number of coastal points exhibits logarithmic fractal behaviour.a Given his role as Editor of this journal, Joseph O. Indekeu had no involvement in the peer-review of articles for which he was an author and had no access to information regarding their peer-review. Full responsibility for the peer-review process for this article was delegated to another Editor.

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Section: Discussionmentioning

confidence: 99%

Coastlines and percolation in a model for hierarchical random deposition

Berx

Bervoets

Giuraniuc

et al. 2021

Physica A: Statistical Mechanics and its Applications

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“…The concept of acoustic metamaterials is not limited only to locally resonant materials or periodic structures. Several other types of acoustic metamaterials have been reported, such as coiling-up space type AMs [59,60], split-ring type AMs, topological acoustics [61], fractal acoustic metamaterials [62][63][64][65][66], helical-structured metamaterials [67,68], and acoustic metasurfaces [69,70]. For coiling-up space type acoustic metamaterials, the incident acoustic waves are confined in coiled subwavelength cross-section channels, thereby resulting in extraordinary acoustic properties such as double negativity and near-zero index to a high effective refractive index of unit cells [71,72].…”

Section: Acoustic Metamaterials: a Brief Overviewmentioning

confidence: 99%

Recent Advances in Acoustic Metamaterials for Simultaneous Sound Attenuation and Air Ventilation Performances

Kumar¹,

Lee²

2020

Crystals

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In the past two decades, acoustic metamaterials have garnered much attention owing to their unique functional characteristics, which are difficult to find in naturally available materials. The acoustic metamaterials have demonstrated excellent acoustical characteristics that paved a new pathway for researchers to develop effective solutions for a wide variety of multifunctional applications, such as low-frequency sound attenuation, sound wave manipulation, energy harvesting, acoustic focusing, acoustic cloaking, biomedical acoustics, and topological acoustics. This review provides an update on the acoustic metamaterials’ recent progress for simultaneous sound attenuation and air ventilation performances. Several variants of acoustic metamaterials, such as locally resonant structures, space-coiling, holey and labyrinthine metamaterials, and Fano resonant materials, are discussed briefly. Finally, the current challenges and future outlook in this emerging field are discussed as well.

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“…However, the actual focus began in 2000, when Smith [ 5 ] demonstrated a composite medium that exhibits a frequency region in the microwave regime with simultaneously negative values of effective permeability and permittivity. Since then, artificially constructed metamaterials have achieved unprecedented development in the fields of electromagnetics [ 6 , 7 , 8 ], optics [ 9 , 10 , 11 ], mechanics [ 12 , 13 , 14 ], and acoustics [ 15 , 16 , 17 ].…”

Section: Introductionmentioning

confidence: 99%

Broadband Sound Insulation and Dual Equivalent Negative Properties of Acoustic Metamaterial with Distributed Piezoelectric Resonators

Zhang

Wang

et al. 2022

Materials

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Aiming at the unsatisfactory sound transmission loss (STL) of thin-plate structures in the low-mid frequency range, this paper proposes an acoustic insulation metamaterial with distributed piezoelectric resonators. A complete acoustic prediction model is established based on the effective medium method and classical plate theory, and the correctness is verified by the STL simulation results of the corresponding acoustic-structure fully coupled finite-element model. Moreover, the intrinsic relationship between the dual equivalent negative properties and STLs is investigated to reveal the insulation mechanisms of this metamaterial. Then, the influence of the geometric and material parameters on the double equivalent negative characteristics is studied to explore the broadband STL for distributed multi-modal resonant energy-dissipation modes in the frequency band of interest. The results show that the two acoustic insulation crests correspond to the dual equivalent negative performances, and the sound insulation in the low-mid frequency range is improved by more than 5 dB compared with that of the substrate, even up to 44.49 dB.

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Hilbert fractal acoustic metamaterials with negative mass density and bulk modulus on subwavelength scale

Cited by 50 publications

References 59 publications

Coastlines and percolation in a model for hierarchical random deposition

Coastlines and percolation in a model for hierarchical random deposition

Recent Advances in Acoustic Metamaterials for Simultaneous Sound Attenuation and Air Ventilation Performances

Broadband Sound Insulation and Dual Equivalent Negative Properties of Acoustic Metamaterial with Distributed Piezoelectric Resonators

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