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Shock and Vibration
Volume 2014, Article ID 189539, 9 pages
http://dx.doi.org/10.1155/2014/189539
Review Article

Phononic First Band Gap of Quaternary Layered Periodic Structure with the Lumped-Mass Method

1Hubei Automotive Structural Engineering Center of Noise & Vibration, Hubei University of Technology, Wuhan 430068, China
2The Institute of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

Received 20 January 2013; Accepted 5 February 2014; Published 27 February 2014

Academic Editor: Nuno Maia

Copyright © 2014 Chen Yuan 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. J. D. Achenbach and M. Kitahara, “Reflection and transmission of an obliquely incident wave by an array of spherical cavities ?” Journal of the Acoustical Society of America, vol. 80, pp. 1209–1214, 1986. View at Google Scholar
  2. J. D. Achenbach and M. Kitahara, “Harmonic waves in a solid with a periodic distribution of spherical cavities,” Journal of the Acoustical Society of America, vol. 81, pp. 595–598, 1987. View at Google Scholar
  3. M. M. Sigalas and E. N. Economou, “Elastic and acoustic wave band structure,” Journal of Sound and Vibration, vol. 158, no. 2, pp. 377–382, 1992. View at Google Scholar · View at Scopus
  4. M. Sigalas and E. N. Economou, “Band structure of elastic waves in two dimensional systems,” Solid State Communications, vol. 86, no. 3, pp. 141–143, 1993. View at Google Scholar · View at Scopus
  5. M. S. Kushwaha, P. Halevi, G. Martínez, L. Dobrzynski, and B. Djafari-Rouhani, “Theory of acoustic band structure of periodic elastic composites,” Physical Review B, vol. 49, no. 4, pp. 2313–2322, 1994. View at Publisher · View at Google Scholar · View at Scopus
  6. C.-S. Kee, J.-E. Kim, H. Y. Park, K. J. Chang, and H. Lim, “Essential role of impedance in the formation of acoustic band gaps,” Journal of Applied Physics, vol. 87, no. 4, pp. 1593–1596, 2000. View at Google Scholar · View at Scopus
  7. R. Esquivel-Sirvent and G. H. Cocoletzi, “Band structure for the propagation of elastic waves in superlattices,” Journal of the Acoustical Society of America, vol. 95, no. 1, pp. 86–90, 1994. View at Google Scholar · View at Scopus
  8. M. I. Hussein, G. M. Hulbert, and R. A. Scott, “Dispersive elastodynamics of 1D banded materials and structures: analysis,” Journal of Sound and Vibration, vol. 289, no. 4-5, pp. 779–806, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. M. I. Hussein, G. M. Hulbert, and R. A. Scott, “Dispersive elastodynamics of 1D banded materials and structures: design,” Journal of Sound and Vibration, vol. 307, no. 3–5, pp. 865–893, 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. Y. P. Zhao and P. J. Wei, “The band gap of 1D viscoelastic phononic crystal,” Computational Materials Science, vol. 46, no. 3, pp. 603–606, 2009. View at Publisher · View at Google Scholar · View at Scopus
  11. M.-L. Wu, L.-Y. Wu, W.-P. Yang, and L.-W. Chen, “Elastic wave band gaps of one-dimensional phononic crystals with functionally graded materials,” Smart Materials and Structures, vol. 18, no. 11, Article ID 115013, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. P. D. Sesion Jr., E. L. Albuquerque, C. Chesman, and V. N. Freire, “Acoustic phonon transmission spectra in piezoelectric AlN/GaN Fibonacci phononic crystals,” European Physical Journal B, vol. 58, no. 4, pp. 379–387, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. F.-M. Li, Y.-Z. Wang, B. Fang, and Y.-S. Wang, “Propagation and localization of two-dimensional in-plane elastic waves in randomly disordered layered piezoelectric phononic crystals,” International Journal of Solids and Structures, vol. 44, no. 22-23, pp. 7444–7456, 2007. View at Publisher · View at Google Scholar · View at Scopus
  14. F.-M. Li, M.-Q. Xu, and Y.-S. Wang, “Frequency-dependent localization length of SH-wave in randomly disordered piezoelectric phononic crystals,” Solid State Communications, vol. 141, no. 5, pp. 296–301, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. Y.-Z. Wang, F.-M. Li, W.-H. Huang, and Y.-S. Wang, “The propagation and localization of Rayleigh waves in disordered piezoelectric phononic crystals,” Journal of the Mechanics and Physics of Solids, vol. 56, no. 4, pp. 1578–1590, 2008. View at Publisher · View at Google Scholar · View at Scopus
  16. Y.-Z. Wang, F.-M. Li, K. Kishimoto, Y.-S. Wang, and W.-H. Huang, “Wave localization in randomly disordered layered three-component phononic crystals with thermal effects,” Archive of Applied Mechanics, vol. 80, no. 6, pp. 629–640, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. H. Policarpo, M. M. Neves, and A. M. R. Ribeiro, “Dynamical response of a multi-laminated periodic bar: analytical, numerical and experimental study,” Shock and Vibration, vol. 17, no. 4-5, pp. 521–535, 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. 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
  19. G. Wang, J. Wen, Y. Liu, and X. 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, pp. 1–184302, 2004. View at Publisher · View at Google Scholar · View at Scopus
  20. D. Richards and D. J. Pines, “Passive reduction of gear mesh vibration using a periodic drive shaft,” Journal of Sound and Vibration, vol. 264, no. 2, pp. 317–342, 2003. View at Publisher · View at Google Scholar · View at Scopus