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Shock and Vibration Volume 2018 ,2018-01-24
Investigation on the Band Gap and Negative Properties of Concentric Ring Acoustic Metamaterial
Research Article
Meng Chen 1 , 2 Dan Meng 1 , 2 Heng Jiang 1 , 2 Yuren Wang 1 , 2
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DOI:10.1155/2018/1369858
Received 2017-07-20, accepted for publication 2017-12-24, Published 2017-12-24
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摘要

The acoustic characteristics of 2D single-oscillator, dual-oscillator, and triple-oscillator acoustic metamaterials were investigated based on concentric ring structures using the finite element method. For the single-oscillator, dual-oscillator, and triple-oscillator models investigated here, the dipolar resonances of the scatterer always induce negative effective mass density, preventing waves from propagating in the structure, thus forming the band gap. As the number of oscillators increases, relative movements between the oscillators generate coupling effect; this increases the number of dipolar resonance modes, causes negative effective mass density in more frequency ranges, and increases the number of band gaps. It can be seen that the number of oscillators in the cell is closely related to the number of band gaps due to the coupling effect, when the filling rate is of a certain value.

授权许可

Copyright © 2018 Meng Chen et al. 2018
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

图表

Cross-sectional views of 2D acoustic metamaterials in single-oscillator, dual-oscillator, and triple-oscillator systems (a–c); units in square lattice arrangement (lattice constant = 10 mm) and schematic diagram of the first Brillouin zone (d). Note. Shaded area is the irreducible Brillouin zone. Points Γ, X, and M are irreducible Brillouin vertexes.

Cross-sectional views of 2D acoustic metamaterials in single-oscillator, dual-oscillator, and triple-oscillator systems (a–c); units in square lattice arrangement (lattice constant = 10 mm) and schematic diagram of the first Brillouin zone (d). Note. Shaded area is the irreducible Brillouin zone. Points Γ, X, and M are irreducible Brillouin vertexes.

Cross-sectional views of 2D acoustic metamaterials in single-oscillator, dual-oscillator, and triple-oscillator systems (a–c); units in square lattice arrangement (lattice constant = 10 mm) and schematic diagram of the first Brillouin zone (d). Note. Shaded area is the irreducible Brillouin zone. Points Γ, X, and M are irreducible Brillouin vertexes.

Cross-sectional views of 2D acoustic metamaterials in single-oscillator, dual-oscillator, and triple-oscillator systems (a–c); units in square lattice arrangement (lattice constant = 10 mm) and schematic diagram of the first Brillouin zone (d). Note. Shaded area is the irreducible Brillouin zone. Points Γ, X, and M are irreducible Brillouin vertexes.

Band structure of single-oscillator acoustic metamaterial in the ΓX direction (a); transmission characteristic curve in the ΓX direction (b); normalized effective mass density, effective bulk modulus, and effective shear modulus (c–e). The blue regions represent the positions of band gaps. P and S represent a compression wave (p-wave) and shear wave (s-wave), respectively.

Band structure of single-oscillator acoustic metamaterial in the ΓX direction (a); transmission characteristic curve in the ΓX direction (b); normalized effective mass density, effective bulk modulus, and effective shear modulus (c–e). The blue regions represent the positions of band gaps. P and S represent a compression wave (p-wave) and shear wave (s-wave), respectively.

Band structure of single-oscillator acoustic metamaterial in the ΓX direction (a); transmission characteristic curve in the ΓX direction (b); normalized effective mass density, effective bulk modulus, and effective shear modulus (c–e). The blue regions represent the positions of band gaps. P and S represent a compression wave (p-wave) and shear wave (s-wave), respectively.

Band structure of single-oscillator acoustic metamaterial in the ΓX direction (a); transmission characteristic curve in the ΓX direction (b); normalized effective mass density, effective bulk modulus, and effective shear modulus (c–e). The blue regions represent the positions of band gaps. P and S represent a compression wave (p-wave) and shear wave (s-wave), respectively.

Band structure of single-oscillator acoustic metamaterial in the ΓX direction (a); transmission characteristic curve in the ΓX direction (b); normalized effective mass density, effective bulk modulus, and effective shear modulus (c–e). The blue regions represent the positions of band gaps. P and S represent a compression wave (p-wave) and shear wave (s-wave), respectively.

Vibration modes at lower edge (a) and upper edge (b) of the first band gap of the single-oscillator acoustic metamaterial system. The color bar represents the normalized displacement.

Vibration modes at lower edge (a) and upper edge (b) of the first band gap of the single-oscillator acoustic metamaterial system. The color bar represents the normalized displacement.

Band structure of dual-oscillator acoustic metamaterial in the ΓX direction (a); transmission characteristic curve in the ΓX direction (b); normalized effective mass density, effective bulk modulus, and effective shear modulus (c–e).

Band structure of dual-oscillator acoustic metamaterial in the ΓX direction (a); transmission characteristic curve in the ΓX direction (b); normalized effective mass density, effective bulk modulus, and effective shear modulus (c–e).

Band structure of dual-oscillator acoustic metamaterial in the ΓX direction (a); transmission characteristic curve in the ΓX direction (b); normalized effective mass density, effective bulk modulus, and effective shear modulus (c–e).

Band structure of dual-oscillator acoustic metamaterial in the ΓX direction (a); transmission characteristic curve in the ΓX direction (b); normalized effective mass density, effective bulk modulus, and effective shear modulus (c–e).

Band structure of dual-oscillator acoustic metamaterial in the ΓX direction (a); transmission characteristic curve in the ΓX direction (b); normalized effective mass density, effective bulk modulus, and effective shear modulus (c–e).

Vibration modes at the lower edge (a) and upper edge (b) of the first band gap; vibration modes at the lower edge (c) and upper edge (d) of the second band gap of the dual-oscillator acoustic metamaterial system. The color bar represents the normalized displacement.

Vibration modes at the lower edge (a) and upper edge (b) of the first band gap; vibration modes at the lower edge (c) and upper edge (d) of the second band gap of the dual-oscillator acoustic metamaterial system. The color bar represents the normalized displacement.

Vibration modes at the lower edge (a) and upper edge (b) of the first band gap; vibration modes at the lower edge (c) and upper edge (d) of the second band gap of the dual-oscillator acoustic metamaterial system. The color bar represents the normalized displacement.

Vibration modes at the lower edge (a) and upper edge (b) of the first band gap; vibration modes at the lower edge (c) and upper edge (d) of the second band gap of the dual-oscillator acoustic metamaterial system. The color bar represents the normalized displacement.

Band structure of triple-oscillator acoustic metamaterial in the ΓX direction (a); transmission characteristic curve in the ΓX direction (b); normalized effective mass density, effective bulk modulus, and effective shear modulus (c–e).

Band structure of triple-oscillator acoustic metamaterial in the ΓX direction (a); transmission characteristic curve in the ΓX direction (b); normalized effective mass density, effective bulk modulus, and effective shear modulus (c–e).

Band structure of triple-oscillator acoustic metamaterial in the ΓX direction (a); transmission characteristic curve in the ΓX direction (b); normalized effective mass density, effective bulk modulus, and effective shear modulus (c–e).

Band structure of triple-oscillator acoustic metamaterial in the ΓX direction (a); transmission characteristic curve in the ΓX direction (b); normalized effective mass density, effective bulk modulus, and effective shear modulus (c–e).

Band structure of triple-oscillator acoustic metamaterial in the ΓX direction (a); transmission characteristic curve in the ΓX direction (b); normalized effective mass density, effective bulk modulus, and effective shear modulus (c–e).

Vibration modes at lower edge (a) and upper edge (b) of the first band gap, at lower edge (c) and upper edge (d) of the second band gap, and at lower edge (e) and upper edge (f) of the third band gap in the triple-oscillator acoustic metamaterial system. The color bar represents the normalized displacement.

Vibration modes at lower edge (a) and upper edge (b) of the first band gap, at lower edge (c) and upper edge (d) of the second band gap, and at lower edge (e) and upper edge (f) of the third band gap in the triple-oscillator acoustic metamaterial system. The color bar represents the normalized displacement.

Vibration modes at lower edge (a) and upper edge (b) of the first band gap, at lower edge (c) and upper edge (d) of the second band gap, and at lower edge (e) and upper edge (f) of the third band gap in the triple-oscillator acoustic metamaterial system. The color bar represents the normalized displacement.

Vibration modes at lower edge (a) and upper edge (b) of the first band gap, at lower edge (c) and upper edge (d) of the second band gap, and at lower edge (e) and upper edge (f) of the third band gap in the triple-oscillator acoustic metamaterial system. The color bar represents the normalized displacement.

Vibration modes at lower edge (a) and upper edge (b) of the first band gap, at lower edge (c) and upper edge (d) of the second band gap, and at lower edge (e) and upper edge (f) of the third band gap in the triple-oscillator acoustic metamaterial system. The color bar represents the normalized displacement.

Vibration modes at lower edge (a) and upper edge (b) of the first band gap, at lower edge (c) and upper edge (d) of the second band gap, and at lower edge (e) and upper edge (f) of the third band gap in the triple-oscillator acoustic metamaterial system. The color bar represents the normalized displacement.

Numerical model for transmission computation. The color represents the displacement.

通讯作者

1. Heng Jiang.Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China, cas.cn;University of Chinese Academy of Sciences, Beijing 100049, China, ucas.ac.cn.hengjiang@imech.ac.cn
2. Yuren Wang.Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China, cas.cn;University of Chinese Academy of Sciences, Beijing 100049, China, ucas.ac.cn.yurenwang@imech.ac.cn

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Meng Chen,Dan Meng,Heng Jiang,Yuren Wang. Investigation on the Band Gap and Negative Properties of Concentric Ring Acoustic Metamaterial. Shock and Vibration ,Vol.2018(2018)

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