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Research Papers

Elastic Wave Band Structures and Defect States in a Periodically Corrugated Piezoelectric Plate

[+] 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 Lab 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 March 17, 2014; final manuscript received April 15, 2014; accepted manuscript posted April 25, 2014; published online May 7, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(8), 081005 (May 07, 2014) (6 pages) Paper No: JAM-14-1116; doi: 10.1115/1.4027487 History: Received March 17, 2014; Revised April 15, 2014; Accepted April 25, 2014

The band structures of shear horizontal (SH) waves in a periodically corrugated piezoelectric plate (PCPP) are studied by using the supercell plane wave expansion (SC-PWE) method. The effect of plate symmetry on the defect state caused by a defect in the plate is investigated in detail. The PCPPs with different types of symmetry give rise to different kinds of band gaps and the associated defect states. The increase of defect size lowers the frequency of defect bands, and it can be used to tune the narrow-passband frequencies in acoustic band gaps. Symmetry breaking is also introduced by reducing the lower corrugation depth of the PCPP. Results show that symmetry breaking leads to both the appearance and disappearance of new kinds of gaps and the corresponding defect bands in these gaps.

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Figures

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Fig. 1

Sketch of PCPPs, (a) perfect and symmetric, (b) perfect and antisymmetric, (c) defective and symmetric, and (d) defective and antisymmetric

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Fig. 2

Supercells with a defect for (a) the symmetric plate and (b) the antisymmetric plate

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Fig. 3

Band structures for perfect PCPPs with a˜ = 0.9, b˜ = 0.45, (a) symmetric plate with h˜1 = h˜2 = 0.2, (b) antisymmetric plate with h˜1 = h˜2 = 0.2, (c) symmetric plate with h˜1 = h˜2 = 0.4, and (d) antisymmetric plate with h˜1 = h˜2 = 0.4

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Fig. 4

Band structures for (a) symmetric plate and (b) antisymmetric plate for different values of β, and h˜1 = h˜2 = 0.4, a˜ = 0.9, and b˜ = 0.45

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Fig. 5

Normalized defect mode shapes of mechanical displacement W˜ at the Γ point for the lower Bragg defect mode, the higher Bragg defect mode, and the non-Bragg defect mode, with β = 0.4, h˜1 = h˜2 = 0.4, a˜ = 0.9, and b˜ = 0.45

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Fig. 6

Band structures for original (a) symmetric plate and (b) antisymmetric plate with varying h˜2, with β = 0.4, h˜1 = 0.4, a˜ = 0.9, and b˜ = 0.45

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Fig. 7

Normalized defect mode shapes of mechanical displacement W˜ at the Γ point for (a) the lower Bragg defect mode in the original symmetric plate and (b) the non-Bragg defect mode in the original antisymmetric plate with varying h˜2, and β = 0.4, h˜1 = 0.4, a˜ = 0.9, and b˜ = 0.45

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Fig. 8

Piezoelectric effect on band structures for (a) symmetric plate and (b) antisymmetric plate, and β = 0.4, h˜1 = h˜2 = 0.4, a˜ = 0.9, and b˜ = 0.45

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