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Shock and Vibration
Volume 2018, Article ID 1369858, 12 pages
https://doi.org/10.1155/2018/1369858
Research Article

Investigation on the Band Gap and Negative Properties of Concentric Ring Acoustic Metamaterial

1Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
2University of Chinese Academy of Sciences, Beijing 100049, China

Correspondence should be addressed to Heng Jiang; nc.ca.hcemi@gnaijgneh and Yuren Wang; nc.ca.hcemi@gnawneruy

Received 20 July 2017; Revised 4 December 2017; Accepted 24 December 2017; Published 24 January 2018

Academic Editor: Marcello Vanali

Copyright © 2018 Meng Chen 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. Y. F. Wang, Y. S. Wang, and L. Wang, “Two-dimensional ternary locally resonant phononic crystals with a comblike coating,” Journal of Physics D: Applied Physics, vol. 47, Article ID 015502, 2014. View at Google Scholar
  2. T. Y. Chiang, L.-Y. Wu, C.-N. Tsai, and L. W. Chen, “A multilayered acoustic hyperlens with acoustic metamaterials,” Applied Physics A, vol. 103, pp. 355–359, 2011. View at Google Scholar
  3. Y. Lai, Y. Wu, P. Sheng, and Z. Q. Zhang, “Hybrid elastic solids,” Nature Materials, vol. 10, no. 8, pp. 620–624, 2011. View at Google Scholar
  4. Z. Liu, X. Zhang, Y. 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
  5. Z. Liu, C. T. Chan, and P. Sheng, “Analytic model of phononic crystals with local resonances,” Physical Review B, vol. 71, no. 1, Article ID 014103, 2005. View at Publisher · View at Google Scholar · View at Scopus
  6. Z. Yang, J. Mei, M. Yang, N. H. Chan, and P. Sheng, “Membrane-type acoustic metamaterial with negative dynamic mass,” Physical Review Letters, vol. 101, no. 20, Article ID 204301, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. N. Fang, D. Xi, J. Xu et al., “Ultrasonic metamaterials with negative modulus,” Nature Materials, vol. 5, no. 6, pp. 452–456, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. X. Zhou and G. Hu, “Analytic model of elastic metamaterials with local resonances,” Physical Review B, vol. 79, Article ID 195109, 2009. View at Publisher · View at Google Scholar
  9. Y. Wu, Y. Lai, and Z. Q. Zhang, “Effective medium theory for elastic metamaterials in two dimensions,” Physical Review B, vol. 76, Article ID 205313, 2007. View at Publisher · View at Google Scholar
  10. Y. Ding, Z. Liu, C. Qiu, and J. Shi, “Metamaterial with simultaneously negative bulk modulus and mass density,” Physical Review Letters, vol. 99, no. 9, Article ID 093904, 2007. View at Publisher · View at Google Scholar · View at Scopus
  11. J. Li and C. Chan, “Double-negative acoustic metamaterial,” Physical Review E, vol. 70, Article ID 055602, 2004. View at Publisher · View at Google Scholar
  12. K. Deng, Y. Ding, Z. He, H. Zhao, J. Shi, and Z. Liu, “Theoretical study of subwavelength imaging by acoustic metamaterial slabs,” Journal of Applied Physics, vol. 105, no. 12, p. 124909, 2009. View at Publisher · View at Google Scholar
  13. M. B. Assouar and M. Oudich, “Enlargement of a locally resonant sonic band gap by using double-sides stubbed phononic plates,” Applied Physics Letters, vol. 100, no. 12, Article ID 123506, 2012. View at Publisher · View at Google Scholar
  14. Y. Xiao, B. R. MacE, J. Wen, and X. Wen, “Formation and coupling of band gaps in a locally resonant elastic system comprising a string with attached resonators,” Physics Letters A, vol. 375, no. 12, pp. 1485–1491, 2011. View at Publisher · View at Google Scholar · View at Scopus
  15. P. Yeh, A. Yariv, and E. Maron, “Theory of bragg fiber,” Journal of the Optical Society of America, vol. 68, no. 9, pp. 1196–1201, 1978. View at Publisher · View at Google Scholar · View at Scopus
  16. A. Kitagawa and J.-I. Sakai, “Bloch theorem in cylindrical coordinates and its application to a Bragg fiber,” Physical Review A, vol. 80, no. 3, Article ID 033802, pp. 2962–2964, 2009. View at Publisher · View at Google Scholar
  17. H. Larabi, Y. Pennec, B. Djafari-Rouhani, and J. O. Vasseur, “Multicoaxial cylindrical inclusions in locally resonant phononic crystals,” Physical Review E, vol. 75, no. 6, Article ID 066601, 2007. View at Publisher · View at Google Scholar · View at Scopus
  18. D. Torrent and J. Sánchezdehesa, “Radial wave crystals: radially periodic structures from anisotropic metamaterials for engineering acoustic or electromagnetic waves,” Physical Review Letters, vol. 103, Article ID 064301, 2009. View at Google Scholar
  19. Z. Xu, F. Wu, and Z. Guo, “Low frequency phononic band structures in two-dimensional arc-shaped phononic crystals,” Physics Letters A, vol. 376, pp. 2256–2263, 2012. View at Google Scholar
  20. X. Zhou and C. Chen, “Tuning the locally resonant phononic band structures of two-dimensional periodic electroactive composites,” Physica B: Condensed Matter, vol. 431, pp. 23–31, 2013. View at Publisher · View at Google Scholar
  21. X. Zhang, Y. Liu, F. Wu, and Z. Liu, “Large two-dimensional band gaps in three-component phononic crystals,” Physics Letters A, vol. 317, no. 1-2, pp. 144–149, 2003. View at Publisher · View at Google Scholar
  22. G. Wang, L. Shao, Y. Liu, and J. Wen, Chin. Phys, vol. 15, pp. 1843–1848, 2006. View at Publisher · View at Google Scholar
  23. Y. Wu, Y. Lai, and Z. Zhang, “Effective medium theory for elastic metamaterials in two dimensions,” Physical Review B, vol. 76, Article ID 205313, 2007. View at Publisher · View at Google Scholar
  24. P. Sheng, J. Mei, Z. Liu, and W. Wen, “Dynamic mass density and acoustic metamaterials,” Physica B: Condensed Matter, vol. 394, no. 2, pp. 256–261, 2007. View at Publisher · View at Google Scholar · View at Scopus
  25. B. Popa and S. A. Cummer, “Design and characterization of broadband acoustic composite metamaterials,” Physical Review B, vol. 80, no. 17, Article ID 174303, 2009. View at Publisher · View at Google Scholar
  26. L. Zigoneanu, B. Popa, A. F. Starr, and S. A. Cummer, “Design and measurements of a broadband two-dimensional acoustic metamaterial with anisotropic effective mass density,” Journal of Applied Physics, vol. 109, no. 5, p. 054906, 2011. View at Publisher · View at Google Scholar
  27. R. E. Camley, B. Djafari-Rouhani, L. Dobrzynski, and A. A. Maradudin, “Sagittal elastic waves in infinite and semi-infinite superlattices,” Physical Review B, vol. 28, pp. 1711–1720, 1983. View at Google Scholar
  28. Z. Liu, C. T. Chan, P. Sheng, A. L. Goertzen, and J. H. Page, “Elastic wave scattering by periodic structures of spherical objects: theory and experiment,” Physical Review B, vol. 62, no. 4, pp. 2446–2457, 2000. View at Publisher · View at Google Scholar · View at Scopus
  29. I. E. Psarobas, N. Stefanou, and A. Modinos, “Scattering of elastic waves by periodic arrays of spherical bodies,” Physical Review B, vol. 62, no. 1, pp. 278–291, 2000. View at Publisher · View at Google Scholar
  30. Y. Tanaka, Y. Tomoyasu, and S.-I. Tamura, “Band structure of acoustic waves in phononic lattices: two-dimensional composites with large acoustic mismatch,” Physical Review B, vol. 62, no. 11, pp. 7387–7392, 2000. View at Publisher · View at Google Scholar · View at Scopus
  31. J. S. Jensen, “Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures,” Journal of Sound and Vibration, vol. 266, no. 5, pp. 1053–1078, 2003. View at Publisher · View at Google Scholar · View at Scopus
  32. G. Wang, J. H. Wen, Y. Z. Liu, and X. S. Wen, “Lumped-mass method for the study of band structure in two-dimensional phononic crystals,” Physical Review B, vol. 69, no. 18, Article ID 184302, 2004. View at Publisher · View at Google Scholar · View at Scopus
  33. D. Krattiger and M. I. Hussein, “Bloch mode synthesis: ultrafast methodology for elastic band-structure calculations,” Physical Review E, vol. 90, no. 6, Article ID 069904, 2014. View at Google Scholar
  34. J. Wen, H. Zhao, L. Lv, B. Yuan, G. Wang, and X. Wen, “Effects of locally resonant modes on underwater sound absorption in viscoelastic materials,” The Journal of the Acoustical Society of America, vol. 130, no. 3, pp. 1201–1208, 2011. View at Publisher · View at Google Scholar · View at Scopus
  35. I. A. Veres, T. Berer, and O. Matsuda, “Complex band structures of two dimensional phononic crystals: analysis by the finite element method,” Journal of Applied Physics, vol. 114, no. 8, Article ID 083519, 2013. View at Publisher · View at Google Scholar · View at Scopus
  36. X. N. Liu, G. K. Hu, G. L. Huang, and C. T. Sun, “An elastic metamaterial with simultaneously negative mass density and bulk modulus,” Applied Physics Letters, vol. 98, no. 25, p. 251907, 2011. View at Publisher · View at Google Scholar
  37. M. Hirsekorn, “Small-size sonic crystals with strong attenuation bands in the audible frequency range,” Applied Physics Letters, vol. 84, no. 17, pp. 3364–3366, 2004. View at Publisher · View at Google Scholar
  38. Y. F. Wang, Y. S. Wang, and V. Laude, “Wave propagation in two-dimensional viscoelastic metamaterials,” Physical Review B, vol. 92, Article ID 104110, 2015. View at Google Scholar
  39. Y. F. Wang, V. Laude, and Y. S. Wang, “Coupling of evanescent and propagating guided modes in locally resonant phononic crystals,” Journal of Physics D: Applied Physics, vol. 47, no. 47, Article ID 475502, 2014. View at Publisher · View at Google Scholar
  40. P. G. Domadiya, E. Manconi, M. Vanali, L. V. Andersen, and A. Ricci, “Numerical and experimental investigation of stop-bands in finite and infinite periodic one-dimensional structures,” Journal of Vibration and Control, vol. 22, no. 4, pp. 920–931, 2016. View at Publisher · View at Google Scholar · View at Scopus
  41. 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 Publisher · View at Google Scholar
  42. M. Chen, D. Meng, H. Zhang, H. Jiang, and Y. Wang, “Resonance-coupling effect on broad band gap formation in locally resonant sonic metamaterials,” Wave Motion, vol. 63, pp. 111–119, 2016. View at Publisher · View at Google Scholar · View at Scopus
  43. M. Badreddine Assouar, J.-H. Sun, F.-S. Lin, and J.-C. Hsu, “Hybrid phononic crystal plates for lowering and widening acoustic band gaps,” Ultrasonics, vol. 54, no. 8, pp. 2159–2164, 2014. View at Publisher · View at Google Scholar · View at Scopus
  44. Y. Cheng, J. Y. Xu, and X. J. Liu, “Broad forbidden bands in parallel-coupled locally resonant ultrasonic metamaterials,” Applied Physics Letters, vol. 92, no. 5, p. 051913, 2008. View at Publisher · View at Google Scholar