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Research Papers

Wave Characteristics of Two-Dimensional Hierarchical Hexagonal Lattice Structures

[+] Author and Article Information
Y. L. Xu

State Key Laboratory for Mechanical
Structure Strength and Vibration,
Xi'an Jiaotong University,
Xi'an 710049, China

C. Q. Chen

Department of Engineering Mechanics,
AML & CNMM,
Tsinghua University,
Beijing 100084, China

X. G. Tian

State Key Laboratory for Mechanical
Structure Strength and Vibration,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: tiansu@mail.xjtu.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 23, 2012; final manuscript received July 14, 2013; published online October 24, 2013. Assoc. Editor: Massimo Ruzzene.

J. Vib. Acoust 136(1), 011011 (Oct 24, 2013) (8 pages) Paper No: VIB-12-1186; doi: 10.1115/1.4025550 History: Received June 23, 2012; Revised July 14, 2013

Hierarchical structures are structures that themselves contain structural elements. Hierarchical lattice structures are counterparts of the traditional lattice structures, whose walls are replaced by some kind of structure. In this paper, wave propagation in two-dimensional hierarchical hexagonal lattice structures is calculated by the finite element method with the Bloch theory. Attention is devoted to the comparison of the band gap, wave mode, dispersion surface, and phase and group velocities between the second-order hierarchical hexagonal lattice structures and their first-order traditional counterpart. The results show that the former structures have more band gaps and similar isotropic wave behavior in the low frequency compared to the latter structure. The structure hierarchy is favorable for the periodic lattice structure to filtering or guiding wave at some circumstances to meet the demands of engineering.

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Figures

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Fig. 1

Schematic of the primitive cells of the three hexagonal lattice structures (a) the first-order THLS; (b) the second-order HHLS with sandwiched rectangle struts core; (c) the second-order HHLS with sandwiched triangular struts core

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Fig. 2

(a) The unit cell and the direct lattice vectors of the hexagonal lattice structures; (b) the corresponding reciprocal lattice vectors and the first and irreducible Brillouin zones

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Fig. 6

Phase and group velocities of the first wave mode at iso-frequencies 0.06, 0.12, 0.18 for the hexagonal lattice structures: (a) the first-order THLS; (b) the second-order HHLS with sandwiched rectangular struts core; (c) the second-order HHLS with sandwiched triangular struts core

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Fig. 5

Contour plots of the first and fifth dispersion surfaces for the hexagonal lattice structures: (a,d) the first-order THLS; (b,e) the second-order HHLS with sandwiched rectangular struts core; (c,f) the second-order HHLS with sandwiched triangular struts core

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Fig. 4

Wave modes of the hexagonal lattice structures: (a) the wave modes corresponding to 1-5 bands at point O in k space; (b) the wave modes corresponding to 1-5 bands at the point B in k space

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Fig. 3

Band structures of the hexagonal lattice structures: (a) the first-order THLS; (b) the second-order HHLS with sandwiched rectangular struts core; (c) the second-order HHLS with sandwiched triangular struts core

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