Table of Contents Author Guidelines Submit a Manuscript
Shock and Vibration
Volume 2016 (2016), Article ID 4015363, 12 pages
http://dx.doi.org/10.1155/2016/4015363
Research Article

An Enhanced Plane Wave Expansion Method to Solve Piezoelectric Phononic Crystal with Resonant Shunting Circuits

1Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China
2Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment, Huazhong University of Science and Technology, Wuhan 430074, China
3State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China

Received 28 October 2015; Revised 25 January 2016; Accepted 15 February 2016

Academic Editor: Sergio De Rosa

Copyright © 2016 Ziyang Lian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. I. Hussein, M. J. Leamy, and M. Ruzzene, “Dynamics of phononic materials and structures: historical origins, recent progress, and future outlook,” Applied Mechanics Reviews, vol. 66, no. 4, Article ID 040802, 2014. View at Publisher · View at Google Scholar
  2. M. Liu, P. Li, Y. Zhong, and J. Xiang, “Research on the band gap characteristics of two-dimensional phononic crystals microcavity with local resonant structure,” Shock and Vibration, vol. 2015, Article ID 239832, 8 pages, 2015. View at Publisher · View at Google Scholar
  3. Z. Y. Liu, X. X. Zhang, Y. W. Mao et al., “Locally resonant sonic materials,” Science, vol. 289, no. 5485, pp. 1734–1736, 2000. View at Publisher · View at Google Scholar · View at Scopus
  4. C. Goffaux, J. Sánchez-Dehesa, A. L. Yeyati et al., “Evidence of fano-like interference phenomena in locally resonant materials,” Physical Review Letters, vol. 88, no. 22, Article ID 225502, 2002. View at Google Scholar · View at Scopus
  5. C. Goffaux and J. Sánchez-Dehesa, “Two-dimensional phononic crystals studied using a variational method: application to lattices of locally resonant materials,” Physical Review B, vol. 67, no. 14, Article ID 144301, 2003. View at Publisher · View at Google Scholar
  6. G. Wang, J. W. Wang, S. b. Chen, and J. h. Wen, “Vibration attenuations induced by periodic arrays of piezoelectric patches connected by enhanced resonant shunting circuits,” Smart Materials and Structures, vol. 20, no. 12, Article ID 125019, 2011. View at Publisher · View at Google Scholar · View at Scopus
  7. G. Wang, S. B. Chen, and J. H. Wen, “Low-frequency locally resonant band gaps induced by arrays of resonant shunts with Antoniou's circuit: experimental investigation on beams,” Smart Materials and Structures, vol. 20, no. 1, Article ID 015026, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. S. B. Chen, J. H. Wen, G. Wang, X. Y. Han, and X. S. Wen, “Locally resonant gaps of phononic beams induced by periodic arrays of resonant shunts,” Chinese Physics Letters, vol. 28, no. 9, Article ID 094301, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. S. b. Chen, J. h. Wen, G. Wang, D. L. Yu, and X. s. Wen, “Improved modeling of rods with periodic arrays of shunted piezoelectric patches,” Journal of Intelligent Material Systems and Structures, vol. 23, no. 14, pp. 1613–1621, 2012. View at Publisher · View at Google Scholar · View at Scopus
  10. A. A. Kutsenko, A. L. Shuvalov, O. Poncelet, and A. N. Darinskii, “Tunable effective constants of the one-dimensional piezoelectric phononic crystal with internal connected electrodes,” The Journal of the Acoustical Society of America, vol. 137, no. 2, pp. 606–616, 2015. View at Publisher · View at Google Scholar
  11. A. Baz, “Active control of periodic structures,” Journal of Vibration and Acoustics, vol. 123, no. 4, pp. 472–479, 2001. View at Publisher · View at Google Scholar · View at Scopus
  12. M. Ruzzene and A. Baz, “Active control of wave propagation in periodic fluid-loaded shells,” Smart Materials and Structures, vol. 10, no. 5, pp. 893–906, 2001. View at Publisher · View at Google Scholar · View at Scopus
  13. O. Thorp, M. Ruzzene, and A. Baz, “Attenuation of wave propagation in fluid-loaded shells with periodic shunted piezoelectric rings,” Smart Materials and Structures, vol. 14, no. 4, pp. 594–604, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. A. Singh, D. J. Pines, and A. Baz, “Active/passive reduction of vibration of periodic one-dimensional structures using piezoelectric actuators,” Smart Materials and Structures, vol. 13, no. 4, pp. 698–711, 2004. View at Publisher · View at Google Scholar · View at Scopus
  15. A. Spadoni, M. Ruzzene, and K. Cunefare, “Vibration and wave propagation control of plates with periodic arrays of shunted piezoelectric patches,” Journal of Intelligent Material Systems and Structures, vol. 20, no. 8, pp. 979–990, 2009. View at Publisher · View at Google Scholar · View at Scopus
  16. F. Casadei, M. Ruzzene, L. Dozio, and K. A. Cunefare, “Broadband vibration control through periodic arrays of resonant shunts: experimental investigation on plates,” Smart Materials and Structures, vol. 19, no. 1, Article ID 015002, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Wilm, S. Ballandras, V. Laude, and T. Pastureaud, “A full 3D plane-wave-expansion model for 1–3 piezoelectric composite structures,” Journal of the Acoustical Society of America, vol. 112, no. 3, pp. 943–952, 2002. View at Publisher · View at Google Scholar · View at Scopus
  18. Y. Z. Wang, F. M. Li, K. Kishimoto, Y. S. Wang, and W. H. Huang, “Band gaps of elastic waves in three-dimensional piezoelectric phononic crystals with initial stress,” European Journal of Mechanics—A/Solids, vol. 29, no. 2, pp. 182–189, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. J. q. Li, F. M. Li, Y. S. Wang, and K. Kishimoto, “Wave propagation in two-dimensional disordered piezoelectric phononic crystals,” Acta Mechanica Solida Sinica, vol. 21, no. 6, pp. 507–516, 2008. View at Publisher · View at Google Scholar · View at Scopus
  20. J. O. Vasseur, A. C. Hladky-Hennion, B. Djafari-Rouhani et al., “Waveguiding in two-dimensional piezoelectric phononic crystal plates,” Journal of Applied Physics, vol. 101, no. 11, Article ID 114904, 2007. View at Publisher · View at Google Scholar
  21. Z. G. Huang and C. F. Su, “Band gaps of a two-dimensional periodic graphenelike structure,” Journal of Vibration and Acoustics, vol. 135, no. 4, Article ID 041002, 2013. View at Publisher · View at Google Scholar · View at Scopus
  22. S. B. Chen, G. Wang, J. H. Wen, and X. S. Wen, “Wave propagation and attenuation in plates with periodic arrays of shunted piezo-patches,” Journal of Sound and Vibration, vol. 332, no. 6, pp. 1520–1532, 2013. View at Publisher · View at Google Scholar · View at Scopus
  23. L. X. Dai, S. Jiang, Z. Y. Lian, H. P. Hu, and X. D. Chen, “Locally resonant band gaps achieved by equal frequency shunting circuits of piezoelectric rings in a periodic circular plate,” Journal of Sound and Vibration, vol. 337, pp. 150–160, 2015. View at Publisher · View at Google Scholar · View at Scopus
  24. J.-Y. Yeh, “Control analysis of the tunable phononic crystal with electrorheological material,” Physica B: Condensed Matter, vol. 400, no. 1-2, pp. 137–144, 2007. View at Publisher · View at Google Scholar · View at Scopus
  25. M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, “Acoustic band structure of periodic elastic composites,” Physical Review Letters, vol. 71, no. 13, pp. 2022–2025, 1993. View at Publisher · View at Google Scholar · View at Scopus
  26. Y. Cao, Z. Hou, and Y. Liu, “Convergence problem of plane-wave expansion method for phononic crystals,” Physics Letters A, vol. 327, no. 2-3, pp. 247–253, 2004. View at Publisher · View at Google Scholar · View at Scopus
  27. D. L. Yu, G. Wang, Y. Z. Liu, J. H. Wen, and J. Qiu, “Flexural vibration band gaps in thin plates with two-dimensional binary locally resonant structures,” Chinese Physics, vol. 15, no. 2, pp. 266–271, 2006. View at Publisher · View at Google Scholar · View at Scopus
  28. J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Philadelphia, Pa, USA, 2004.
  29. J. S. Yang, An Introduction to the Theory of Piezoelectricity, Springer, Boston, Mass, USA, 2005.
  30. Y. J. Wang, Z. Y. Lian, J. Wang, M. Yao, and H. P. Hu, “Analysis of a piezoelectric power harvester with adjustable frequency by precise electric field method,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 60, no. 10, pp. 2154–2161, 2013. View at Publisher · View at Google Scholar · View at Scopus
  31. T.-T. Wu, Z.-G. Huang, and S. Lin, “Surface and bulk acoustic waves in two-dimensional phononic crystal consisting of materials with general anisotropy,” Physical Review B, vol. 69, no. 9, Article ID 094301, 2004. View at Google Scholar · View at Scopus
  32. H. P. Hu, Y. T. Hu, and J. S. Yang, “On the inaccuracy of using Mindlin's first-order plate theory for calculating the motional capacitance of a thickness-shear resonator,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 56, no. 1, pp. 7–8, 2009. View at Publisher · View at Google Scholar · View at Scopus