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Research Papers

Acoustic Waves in Two-Dimensional Phononic Crystals With Reticular Geometric Structures

[+] Author and Article Information
Zi-Gui Huang1

Department of Mechanical Design Engineering, National Formosa University, No. 64, Wenhua Road, Huwei Township, Yun-lin County 632, Taiwanzghuang0119@nfu.edu.tw

Zheng-Yu Chen

Department of Mechanical Design Engineering, National Formosa University, No. 64, Wenhua Road, Huwei Township, Yun-lin County 632, Taiwan

1

Corresponding author.

J. Vib. Acoust 133(3), 031011 (Mar 29, 2011) (6 pages) doi:10.1115/1.4003201 History: Received March 18, 2010; Revised September 09, 2010; Published March 29, 2011; Online March 29, 2011

Previous studies on photonic crystals raise the exciting topic of phononic crystals. This paper presents the results of tunable band gaps in the acoustic waves of two-dimensional phononic crystals with reticular geometric structures using the 2D and 3D finite element methods. This paper calculates and discusses the band gap variations of the bulk modes due to different sizes of reticular geometric structures. Results show that adjusting the orientation of the reticular geometric structures can increase or decrease the total elastic band gaps for mixed polarization modes. The band gap phenomena of elastic or acoustic waves can potentially be utilized to achieve vibration-free, high-precision mechanical systems, and sound insulation.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 9

The dispersion relations of reticular geometric structures with a=0.5

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Figure 10

The dispersion relations of reticular geometric structures with a=2.0

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Figure 11

The band gap widths with the scale a from 0.1 to 2.0 when the vertical ranges from 2400 Hz to 5200 Hz

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Figure 12

2D diagrams of unit rectangular lattices in different rotating angles D=30 deg, 45 deg, 75 deg, and 90 deg

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Figure 13

The band gap widths of the rectangular lattices with different rotating angles of reticular geometric structures

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Figure 8

The diagrams of square rectangular lattices with a=0.5 and a=2.0 along the x-axis and the width of the unit cell along the y direction remains 1.0

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Figure 7

The band gap width with parameters c=d varying from 0.1 to 0.9 when the vertical range is selected from 3500 Hz to 4500 Hz

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Figure 6

Eigenmode shapes with 4×4 supercell at M2 in Fig. 4 and M2 is a shear vertical mode

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Figure 5

Eigenmode shapes with 4×4 supercell at M1 in Fig. 4 and M1 is a shear horizontal mode

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Figure 4

The comparison of dispersion relations between the 3D and 2D FEM models with the scales R=h=1, c=0.8, and a=1.2

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Figure 3

Comparison of Bloch calculations between the PWE and FEM methods

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Figure 2

Brillouin regions of the square and rectangular lattices

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Figure 1

(a) Square lattice with lattice spacing R and (b) rectangular lattice with lattice spacing aR along the x-axis and R along the y-axis; (c) a unit cell with reticular structures in a 3D FEM model

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