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Research Papers

Tuning of Acoustic Bandgaps in Phononic Crystals With Helmholtz Resonators

[+] Author and Article Information
Jian-Bao Li

Institute of Engineering Mechanics,
Beijing Jiaotong University,
Beijing 100044, PRC;
Department of Engineering Mechanics,
Taiyuan University of Science and Technology,
Taiyuan, Shanxi 030024, PRC

Yue-Sheng Wang

Institute of Engineering Mechanics,
Beijing Jiaotong University,
Beijing 100044, PRC
e-mail: yswang@bjtu.edu.cn

Chuanzeng Zhang

Department of Civil Engineering,
University of Siegen,
Siegen D-57068, Germany

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received May 28, 2011; final manuscript received January 29, 2013; published online April 25, 2013. Assoc. Editor: Liang-Wu Cai.

J. Vib. Acoust 135(3), 031015 (Jun 25, 2013) (9 pages) Paper No: VIB-11-1118; doi: 10.1115/1.4023812 History: Received May 28, 2011; Revised January 29, 2013

In this paper, acoustic wave propagation in a two- or three-dimensional phononic crystal consisting of Helmholtz resonators embedded in a fluid matrix is studied. The band structures are calculated to discuss the influence of the geometry topology of Helmholtz resonators on the bandgap characteristics. It is shown that a narrow bandgap will appear in the lower frequency range due to the resonance of the Helmholtz resonators. The width and position of this resonance bandgap can be tuned by adjusting the geometrical parameters of the Helmholtz resonator. The position of the resonance bandgap can be evaluated by the resonance frequency of the Helmholtz resonator. A decrease in the size of the opening generally results in a lower position and a smaller width of the bandgap. The system with one opening exhibits a wider bandgap in a lower position than the system with two openings.

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Figures

Grahic Jump Location
Fig. 1

Configurations of the unit cells of phononic crystals in a square lattice with 2D Helmholtz resonators: (a) 2D-HRPC-1 and (b) 2D-HRPC-2

Grahic Jump Location
Fig. 2

Configurations of the unit cells of phononic crystals in a triangular lattice with 2D Helmholtz resonators: (a) 2D-HRPC-1 and (b) 2D-HRPC-2

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Fig. 3

Configuration of the unit cell of phononic crystals with 3D Helmholtz resonators: 3D-HRPC-1

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Fig. 4

Finite element models for the unit cell of phononic crystals in a square lattice with Helmholtz resonators: (a) 2D-HRPC-1 and (b) 2D-HRPC-2

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Fig. 5

Finite element models for the unit cell of phononic crystals in a triangular lattice with Helmholtz resonators: (a) 2D-HRPC-1 and (b) 2D-HRPC-2

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Fig. 6

Finite element models for the unit cell of phononic crystals in a simple cubic lattice with Helmholtz resonators: (a) 3D-HRPC-1 and (b) 3D-HRPC-2

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Fig. 7

The first Brillouin zone for (a) 2D-HRPC with a square lattice, (b) 2D-HRPC with a triangular lattice, and (c) 3D-HRPC with a simple cubic lattice

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Fig. 8

Band structures of the 2D Helmholtz resonator phononic crystals with a square lattice (solid and dashed lines) and the rigid cylinder phononic crystal (scattered dots); the solid and dashed lines represent the modes along Γ-X-M-Γ and Γ-X′-M-Γ, respectively: (a) 2D-HRPC-1 and (b) 2D-HRPC-2

Grahic Jump Location
Fig. 9

Band structures of the 2D Helmholtz resonator phononic crystals with a triangular lattice (solid and dashed lines) and the rigid cylinder phononic crystal (scattered dots); the solid and dashed lines represent the modes along Γ-X-M-Γ and Γ-X′-M-Γ, respectively: (a) 2D-HRPC-1 and (b) 2D-HRPC-2

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Fig. 10

Influence of the slit width on the bandgaps in the square lattice case: (a) 2D-HRPC-1 and (b) 2D-HRPC-2

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Fig. 11

Influence of the slit width on the bandgaps in the triangular lattice case: (a) 2D-HRPC-1 and (b) 2D-HRPC-2

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Fig. 12

Influence of the inner radius on the bandgaps in the square lattice case: (a) 2D-HRPC-1 and (b) 2D-HRPC-2

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Fig. 13

Influence of the inner radius on the bandgaps in the triangular lattice case: (a) 2D-HRPC-1 and (b) 2D-HRPC-2

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Fig. 14

Band structures of the 3D Helmholtz resonator phononic crystal (solid and dashed lines) and the rigid sphere phononic crystal (scattered dots); the solid and dashed lines represent the modes along R-M-Γ-X-M and R-M′-Γ-X′-M′, respectively: (a) 3D-HRPC-1 and (b) 3D-HRPC-2

Grahic Jump Location
Fig. 15

Influence of the size of the open hole on the bandgaps: (a) 3D-HRPC-1 and (b) 3D-HRPC-2

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Fig. 16

Spherical HR with one opening

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