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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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References

Kushwaha, M. S., Halevi, P., Dobrzynski, L., and Djafari-Rouhani, B., 1993, “Acoustic Band Structure of Periodic Elastic Composites,” Phys. Rev. Lett., 71(13), pp. 2022–2025. [CrossRef] [PubMed]
Sigalas, M. M., 1997, “Elastic Wave Band Gaps and Defect States in Two-Dimensional Composites,” J. Acoust. Soc. Am., 101(3), pp. 1256–1261. [CrossRef]
Sigalas, M. M., 1998, “Defect States of Acoustic Waves in a Two-Dimensional Lattice of Solid Cylinders,” J. Appl. Phys., 84(6), pp. 3026–3030. [CrossRef]
Wu, F. G., Liu, Z. Y., and Liu, Y. Y., 2004, “Splitting and Tuning Characteristics of the Point Defect Modes in Two-Dimensional Phononic Crystals,” Phys. Rev. E, 69(6), p. 066609. [CrossRef]
Chen, A. L., Wang, Y. S., Guo, Y. F., and Wang, Z. D., 2008, “Band Structures of Fibonacci Phononic Quasi Crystals,” Solid State Commun., 145(3), pp. 103–108. [CrossRef]
Wang, Y. Z., Li, F. M., Kishimoto, K., Wang, Y. S., and Huang, W. H., 2009, “Elastic Wave Band Gaps in Magnetoelectroelastic Phononic Crystals,” Wave Motion, 46(1), pp. 47–56. [CrossRef]
Khelif, A., Choujaa, A., Benchabane, S., Djafari-Rouhani, B., and Laude, V., 2004, “Guiding and Bending of Acoustic Waves in Highly Confined Phononic Crystal Waveguides,” Appl. Phys. Lett., 84(22), pp. 4400–4402. [CrossRef]
Liu, C. C., Hu, S. L., and Shen, S. P., 2013, “Effect of Flexoelectricity on Band Structures of One-Dimensional Phononic Crystals,” ASME J. Appl. Mech., 81(5), p. 051007. [CrossRef]
Li, F. L., Wang, Y. S., Zhang, C. Z., and Yu, G. L., 2014, “Bandgaps of Two-Dimensional Phononic Crystals With Sliding Interface Conditions,” ASME J. Appl. Mech., 81(6), p. 064501. [CrossRef]
Gei, M., Movchan, A. B., and Bigoni, D., 2009, “Band-Gap Shift and Defect-Induced Annihilation in Prestressed Elastic Structures,” J. Appl. Phys., 105(6), p. 063507. [CrossRef]
Gei, M., Roccabianca, S., and Bacca, M., 2011, “Controlling Bandgap in Electroactive Polymer-Based Structures,” IEEE/ASME Trans. Mechatron., 16(1), pp. 102–107. [CrossRef]
Sun, H. X., Zhang, S. Y., and Shui, X. J., 2012, “A Tunable Acoustic Diode Made by a Metal Plate With Periodical Structure,” Appl. Phys. Lett., 100(10), p. 103507. [CrossRef]
Zhou, S. Y., Gweon, G. H., Fedorov, A. V., First, P. N., De Heer, W. A., Lee, D. H., Guinea, F., Neto, A. C., and Lanzara, A., 2007, “Substrate-Induced Bandgap Opening in Epitaxial Graphene,” Nature Mater., 6(10), pp. 770–775. [CrossRef]
He, X. D., Shen, J. J., Liu, B., and Li, S. J., 2013, “Effects of Symmetry Breaking of Scatterers on Photonic Band Gap in Hexangular-Lattice Photonic Crystal,” Opt. Commun., 303, pp. 8–12. [CrossRef]
Pogrebnyak, V. A., Akray, E., and Kucukaltun, A. N., 2005, “Tunable Gap in the Transmission Spectrum of a Periodic Waveguide,” Appl. Phys. Lett., 86(15), p. 151115. [CrossRef]
Pogrebnyak, V. A., 2004, “Non-Bragg Reflections in a Periodic Waveguide,” Opt. Commun., 232(1–6), pp. 201–207. [CrossRef]
Anderson, P. W., 1958, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev., 109(5), pp. 1492–1505. [CrossRef]
He, Y., Wu, F. G., Yao, Y. W., Zhang, X., Mu, Z. F., Yan, S. Y., and Cheng, C., 2013, “Effect of Defect Configuration on the Localization of Phonons in Two-Dimensional Phononic Crystals,” Phys. Lett. A, 377(12), pp. 889–894. [CrossRef]
Shelke, A., Banerjee, S., Habib, A., Rahani, E. K., Ahmed, R., and Kundu, T., 2013, “Wave Guiding and Wave Modulation Using Phononic Crystal Defects,” J. Intell. Mater. Syst. Struct. (published online). [CrossRef]
Banerjee, S., and Kundu, T., 2006, “Symmetric and Anti-Symmetric Rayleigh–Lamb Modes in Sinusoidally Corrugated Waveguides: An Analytical Approach,” Int. J. Solids Struct., 43(21), pp. 6551–6567. [CrossRef]
Colak, E., Serebryannikov, A. E., Cakmak, A. O., and Ozbay, E., 2013, Experimental Study of Broadband Unidirectional Splitting in Photonic Crystal Gratings With Broken Structural Symmetry, Appl. Phys. Lett., 102(15), p. 151105. [CrossRef]
Bashir, I., Taherzadeh, S., and Attenborough, K., 2013, “Surface Waves Over Periodiclly-Spaced Rectangular Strips,” J. Acoust. Soc. Am., 134(6), pp. 4691–4697. [CrossRef]
Zhu, X. F., Zou, X. Y., Liang, B., and Cheng, J. C., 2010, “One-Way Mode Transmission in One-Dimensional Phononic Crystal Plates,” J. Appl. Phys., 108(12), p. 124909. [CrossRef]
Vasseur, J. O., Deymier, P. A., Djafari-Rouhani, B., Pennec, Y., and Hladky-Hennion, A. C., 2008, “Absolute Forbidden Bands and Waveguiding in Two-Dimensional Phononic Crystal Plates,” Phys. Rev. B, 77(8), p. 085415 [CrossRef]
Hou, Z. L., and Assouar, B. M., 2008, “Modeling of Lamb Wave Propagation in Plate With Two-Dimensional Phononic Crystal Layer Coated on Uniform Substrate Using Plane-Wave-Expansion Method,” Phys. Lett. A, 372(12), pp. 2091–2097. [CrossRef]
Chen, W. Q., 2011, “Surface Effect on Bleustein-Gulyaev Wave in a Piezoelectric Half-Space,” Theor. Appl. Mech. Lett., 1(4), p. 041001. [CrossRef]
Zhu, X. F., Liu, S. C., Xu, T., Wang, T. H., and Cheng, J. C., 2010, “Investigation of a Silicon-Based One-Dimensional Phononic Crystal Plate Via the Super-Cell Plane Wave Expansion Method,” Chin. Phys. B, 19(4), p. 044301. [CrossRef]
Yao, Z. J., Yu, G. L., Wang, Y. S., and Shi, Z. F., 2009, “Propagation of Bending Waves in Phononic Crystal Thin Plates With a Point Defect,” Int. J. Solids Struct., 46(13), pp. 2571–2576. [CrossRef]
Tao, Z. Y., He, W. Y., and Wang, X. L., 2008, “Resonance-Induced Band Gaps in a Periodic Waveguide,” J. Sound Vib., 313(3–5), pp. 830–840. [CrossRef]
Wang, L., Tao, Z. Y., and Wang, X. L., 2011, “Defect States in the Non-Bragg Band Gaps,” Acta Acust., 36(2), pp. 202–206.
Xiao, Y. M., Tao, Z. Y., He, W. Y., and Wang, X. L., 2008, “Non-Bragg Resonance of Surface Water Waves in a Trough With Periodic Walls,” Phys. Rev. E, 78(1), p. 016311. [CrossRef]
Yang, J. S., 2005, An Introduction to the Theory of Piezoelectricity, Springer, New York.

Figures

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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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