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Research Papers

Tuning Band Structures of Two-Dimensional Phononic Crystals With Biasing Fields

[+] Author and Article Information
Y. Huang

Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, China

C. L. Zhang

Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, China
e-mail: zclwei@zju.edu.cn

W. Q. Chen

Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, China;
State Key Laboratory of CAD & CG,
Zhejiang University,
Hangzhou 310058, China

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 5, 2014; final manuscript received June 24, 2014; accepted manuscript posted June 26, 2014; published online July 9, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(9), 091008 (Jul 09, 2014) (7 pages) Paper No: JAM-14-1196; doi: 10.1115/1.4027915 History: Received May 05, 2014; Revised June 24, 2014; Accepted June 26, 2014

The control of band structures of 2D phononic crystals (PCs) composed of piezoelectric inclusions and elastic isotropic matrix with mechanical/electrical biasing fields is theoretically investigated. The theory for small fields superposed on biasing fields and the plane wave expansion (PWE) method is employed to compute the band structures of the PCs under different biasing fields, including the initial shear/normal stress and the initial electric field. We find that the initial shear stress breaks the symmetry of the material. In consequence, the two bands associated with the level repulsion effect are opened near the apparent crosspoint and form a local band gap. On the other hand, the normal initial stress and the biasing electric field change the effective stiffness and shift the positions of band gaps. The observed phenomena show that the biasing fields can be flexibly used to tune the PC devices.

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Figures

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Fig. 1

(a) Unit cell and (b) the Brillouin zone of the two-dimensional PC

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Fig. 2

Band structures of the x1x2-mode for case (1): (a) T˜120=0, (b) T˜120=0.05, (c) T˜120=0.1, and (d) T˜120=0.2

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Fig. 3

Magnification of the windows in Fig. 2: (a) W1 and (b) W2

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Fig. 4

Displacement fields of points (a) P1, (b) P2, (c) P3, and (d) P4 in Fig. 3(a) throughout the unit cell

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Fig. 5

Displacement fields of points (a) Q1, (b) Q5, (c) Q4, (d) Q2, (e) Q6, and (f) Q3 in Fig. 3(b) throughout the unit cell

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Fig. 6

Band structures of the x3-mode in the 2D PC for case (2)

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Fig. 7

Band structures of the 2D PC for case (3): (a) x1x2-mode and (b) x3-mode

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