中国物理B ›› 2006, Vol. 15 ›› Issue (2): 407-411.doi: 10.1088/1009-1963/15/2/029

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Formation mechanism of the low-frequency locally resonant band gap in the two-dimensional ternary phononic crystals

王刚, 刘耀宗, 温激鸿, 郁殿龙   

  1. Institute of Mechatronical Engineering, National University of Defense Technology, Changsha 410073, China,and the PBG Research Center, National University of Defense Technology,Changsha 410073, China
  • 收稿日期:2005-08-26 修回日期:2005-09-13 出版日期:2006-02-20 发布日期:2006-02-20
  • 基金资助:
    Project supported by National Natural Science Foundation of China (Grant No 50575222) and the State Key Development Program for Basic Research of China (Grant No 51307).

Formation mechanism of the low-frequency locally resonant band gap in the two-dimensional ternary phononic crystals

Wang Gang (王刚), Liu Yao-Zong (刘耀宗), Wen Ji-Hong (温激鸿), Yu Dian-Long (郁殿龙)   

  1. Institute of Mechatronical Engineering, National University of Defense Technology, Changsha 410073, China,and the PBG Research Center, National University of Defense Technology,Changsha 410073, China
  • Received:2005-08-26 Revised:2005-09-13 Online:2006-02-20 Published:2006-02-20
  • Supported by:
    Project supported by National Natural Science Foundation of China (Grant No 50575222) and the State Key Development Program for Basic Research of China (Grant No 51307).

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摘要： The low-frequency band gap and the corresponding vibration modes in two-dimensional ternary locally resonant phononic crystals are restudied successfully with the lumped-mass method. Compared with the work of C. Goffaux and J. S\'{a}nchez-Dehesa ({\em Phys. Rev.} B {\bf 67} 14 4301(2003)), it is shown that there exists an error of about 50{\%} in their calculated results of the band structure, and one band is missing in their results. Moreover, the in-plane modes shown in their paper are improper, which results in the wrong conclusion on the mechanism of the ternary locally resonant phononic crystals. Based on the lumped-mass method and better description of the vibration modes according to the band gaps, the locally resonant mechanism in forming the subfrequency gaps is thoroughly analysed. The rule used to judge whether a resonant mode in the phononic crystals can result in a corresponding subfrequency gap is also verified in this ternary case.

关键词: phononic crystals, locally resonant, band gap mechanism

Abstract: The low-frequency band gap and the corresponding vibration modes in two-dimensional ternary locally resonant phononic crystals are restudied successfully with the lumped-mass method. Compared with the work of C. Goffaux and J. Sánchez-Dehesa (Phys. Rev. B 67 14 4301(2003)), it is shown that there exists an error of about 50% in their calculated results of the band structure, and one band is missing in their results. Moreover, the in-plane modes shown in their paper are improper, which results in the wrong conclusion on the mechanism of the ternary locally resonant phononic crystals. Based on the lumped-mass method and better description of the vibration modes according to the band gaps, the locally resonant mechanism in forming the subfrequency gaps is thoroughly analysed. The rule used to judge whether a resonant mode in the phononic crystals can result in a corresponding subfrequency gap is also verified in this ternary case.

Key words: phononic crystals, locally resonant, band gap mechanism

中图分类号:  (Photonic bandgap materials)

  • 42.70.Qs
71.15.-m (Methods of electronic structure calculations) 71.20.-b (Electron density of states and band structure of crystalline solids) 63.20.-e (Phonons in crystal lattices)