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Research Papers

Tuning of Bandgap Structures in Three-Dimensional Kagome-Sphere Lattice

[+] Author and Article Information
Ying Liu

Department of Mechanics,
School of Civil Engineering,
Beijing Jiaotong University,
Beijing 100044, China
e-mail: yliu5@bjtu.edu.cn

Xiu-zhan Sun, Wen-zheng Jiang, Yu Gu

Department of Mechanics,
School of Civil Engineering,
Beijing Jiaotong University,
Beijing 100044, China

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 26, 2013; final manuscript received October 5, 2013; published online January 16, 2014. Assoc. Editor: Michael Leamy.

J. Vib. Acoust 136(2), 021016 (Jan 16, 2014) (8 pages) Paper No: VIB-13-1178; doi: 10.1115/1.4026211 History: Received May 26, 2013; Revised October 05, 2013

In this manuscript, acoustic wave propagation in a novel three-dimensional porous phononic crystal-Kagome lattice, is studied by using finite element method. Firstly, a Kagome-sphere structure is established based on Kagome truss. For lattice with fixed rods (sphere radius varied) or fixed spheres (rod radius varied), the band structures are calculated in order to clarify the influence of geometrical parameters (sphere and rod sizes) on the bandgap characteristics in Kagome-sphere lattice. The vibration modes at the band edges of the lowest bandgaps are investigated with the aim to understand the mechanism of the bandgap generation. It is found that the emergence of the bandgap is due to the local resonant vibration of the unit cell at the adjacent bands. The width and position of this bandgap can be tuned by adjusting the geometrical parameters. An equivalent mass-spring model is proposed and the equivalent system resonance frequency can be evaluated which predicts well the upper and lower edges of the complete bandgaps. Moreover, the critical geometrical parameter is formulated which gives the critical geometrical condition for the opening of the complete bandgaps. The results in this paper are relevant to the bandgap structure design of three-dimensional porous phononic crystals (PPCs).

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Copyright © 2014 by ASME
Topics: Vibration , Energy gap , Rods
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Figures

Grahic Jump Location
Fig. 1

(a) Kagome-sphere lattice; (b) top view of Kagome- sphere lattice; and (c) left view of Kagome-sphere lattice

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Fig. 2

Unit cell of Kagome-sphere lattice with a and c the lattice constants

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Fig. 3

(a) Hexagonal Bravais lattice and (b) reciprocal lattice

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Fig. 4

The first Brillouin zone of the hexagonal Bravais lattice

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Fig. 5

Variation of band structures with respect to the sphere radius. (a) n = 3.6; (b) n = 4.1; (c) n = 4.3; and (d) n = 4.7.

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Fig. 6

Vibration modes of unit cell at the bandgap edges corresponding to Fig. 5 for different spheres. The 3D view, top view (XY cross section) and left view (XZ cross section) are given. (a) n = 4.1; (b) n = 4.3; and (c) n = 4.7.

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Fig. 7

Variation of band structures with respect to the rod radius. (a) m = 0.18; (b) m = 0.27; (c) m = 0.36; and (d) m = 0.44.

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Fig. 8

Vibration modes of unit cell at the bandgap edges corresponding to Fig. 6 for different rods. The 3D view, top view (XY cross section) and left view (XZ cross section) are given. (a) m = 0.18; (b) m = 0.27; and (c) m = 0.36.

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Fig. 9

(a) Variation of the upper and lower edges of complete bandgaps with respect to the normalized sphere radius when rod radius is fixed; and (b) variation of the upper and lower edges of complete bandgaps with respect to the normalized rod radius when sphere radius is fixed

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Fig. 10

Vibration modes of unit cell at the 30th and 31st bands when (a) n = 3.6 and (b) m = 0.44

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Fig. 11

Critical values of Rsphere and Rrod for the opening of complete bandgaps in Kagome-sphere lattice

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