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Research Papers

Acoustic Metamaterial With Fractal Coiling Up Space for Sound Blocking in a Deep Subwavelength Scale

[+] Author and Article Information
Baizhan Xia, Liping Li, Dejie Yu

State Key Laboratory of Advanced Design
and Manufacturing for Vehicle Body,
Hunan University,
Changsha 410082, Hunan, China

Jian Liu

State Key Laboratory of Advanced Design
and Manufacturing for Vehicle Body,
Hunan University,
Changsha 410082, Hunan, China
e-mail: liujian@hnu.edu.cn

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 25, 2016; final manuscript received July 27, 2017; published online September 25, 2017. Assoc. Editor: Mahmoud Hussein.

J. Vib. Acoust 140(1), 011011 (Sep 25, 2017) (8 pages) Paper No: VIB-16-1421; doi: 10.1115/1.4037514 History: Received August 25, 2016; Revised July 27, 2017

Inspired by fractal photonic/phononic crystals, the self-similar fractal technique is applied to design acoustic metamaterial. By replacing the straight channel of coiling up space with a smaller coiling up space, a class of topological architectures with fractal coiling up space is developed. The significant effect of the fractal-inspired hierarchy on the band structure with fractal coiling up space is systematically investigated. Furthermore, sound wave propagation in the acoustic metamaterial with the fractal coiling up space is comprehensively highlighted. Our results show that the acoustic metamaterial with higher-order fractal coiling up space exhibits deep subwavelength bandgaps, in which the sound propagation will be well blocked. Thus, this work provides insights into the role of the fractal hierarchy in regulating the dynamic behavior of the acoustic metamaterial and provides opportunities for the design of a robust filtering device in a subwavelength scale.

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Figures

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Fig. 1

Schematic cross-sectional illustrations of three types of acoustic metamaterials with coiling up spaces: (a) acoustic metamaterial with the first-order coiling up space, (b) acoustic metamaterial with the second-order coiling up space, and (c) acoustic metamaterial with the third-order coiling up space

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Fig. 2

(a) The square lattice. The regular hexagons (the shaded area) represent acoustic metamaterials. The unit cell and the basis vector of the square lattice are marked by square. (b) The Brillouin zone is marked by the shaded area.

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Fig. 3

Band structures of acoustic metamaterials with coiling up spaces in the frequency range [0 Hz, 1000 Hz]: (a) band structure of the first-order acoustic metamaterial, (b) band structure of the second-order acoustic metamaterial, and (c) band structure of the third-order acoustic metamaterial

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Fig. 4

Schematic diagram of physical field settings

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Fig. 5

(a) Transmission coefficient of the first-order acoustic metamaterial. (b) The directional bandgaps of the first-order acoustic metamaterial along with Γ–X. (c) and (d) Sound pressure field distributions at 610 Hz and 885 Hz.

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Fig. 6

(a) Transmission coefficient of the second-order acoustic metamaterial. (b) The directional bandgaps of the second-order acoustic metamaterial along with Γ–X. (c)–(e) Sound pressure field distributions at 330 Hz, 575 Hz, and 915 Hz.

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Fig. 7

(a) Transmission coefficient of the third-order acoustic metamaterial. (b) The directional bandgaps of the third-order acoustic metamaterial along with Γ–X. (c)–(f) Sound pressure field distributions at 230 Hz, 460 Hz, 650 Hz, and 865 Hz.

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Fig. 8

(a) Transmission coefficient of an array composed of 3 × 3 the first-order acoustic metamaterials. (b) and (c) Sound pressure field distributions at 610 Hz and 880 Hz.

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Fig. 9

(a) Transmission loss of an array composed of 3 × 3 the second-order acoustic metamaterials. (b)–(d) Sound pressure field distributions at 330 Hz, 585 Hz, and 925 Hz.

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Fig. 10

(a) Transmission loss of an array composed of 3 × 3 the third-order acoustic metamaterials. (b)–(e) Sound pressure field distributions at 230 Hz, 460 Hz, 655 Hz, and 865 Hz.

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