中国物理B ›› 2016, Vol. 25 ›› Issue (4): 46301-046301.doi: 10.1088/1674-1056/25/4/046301

• CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES • 上一篇    下一篇

Complete low-frequency bandgap in a two-dimensional phononic crystal with spindle-shaped inclusions

Ting Wang(王婷), Hui Wang(王辉), Mei-Ping Sheng(盛美萍), Qing-Hua Qin(秦庆华)   

  1. 1 School of Marine Science and Technology, Northwestern Polytecnical University, Xi'an 710072, China;
    2 Research School of Engineering, Australian National University, Acton, ACT 2601, Australia
  • 收稿日期:2015-09-22 修回日期:2015-10-19 出版日期:2016-04-05 发布日期:2016-04-05
  • 通讯作者: Ting Wang E-mail:WT323@mail.nwpu.edu.cn
  • 基金资助:
    Project supported by the China Scholarship Council.

Complete low-frequency bandgap in a two-dimensional phononic crystal with spindle-shaped inclusions

Ting Wang(王婷)1, Hui Wang(王辉)2, Mei-Ping Sheng(盛美萍)2, Qing-Hua Qin(秦庆华)1   

  1. 1 School of Marine Science and Technology, Northwestern Polytecnical University, Xi'an 710072, China;
    2 Research School of Engineering, Australian National University, Acton, ACT 2601, Australia
  • Received:2015-09-22 Revised:2015-10-19 Online:2016-04-05 Published:2016-04-05
  • Contact: Ting Wang E-mail:WT323@mail.nwpu.edu.cn
  • Supported by:
    Project supported by the China Scholarship Council.

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摘要： A two-dimensional phononic crystal (PC) structure possessing a relatively low frequency range of complete bandgap is presented. The structure is composed of periodic spindle-shaped plumbum inclusions in a rubber matrix which forms a square lattice. The dispersion relation, transmission spectrum and displacement field are studied using the finite element method in conjunction with the Bloch theorem. Numerical results show that the present PC structure can achieve a large complete bandgap in a relatively low frequency range compared with two inclusions of different materials, which is useful in low-frequency noise and vibration control and can be designed as a low frequency acoustic filter and waveguides. Moreover, the transmission spectrum and effective mass are evaluated to validate the obtained band structure. It is interesting to see that within the band gap the effective mass becomes negative, resulting in an imaginary wave speed and wave exponential attenuation. Finally, sensitivity analysis of the effect of geometrical parameters of the presented PC structure on the lowest bandgap is performed to investigate the variations of the bandgap width and frequency.

关键词: phononic crystal, spindle-shaped inclusion, transmission spectrum, bandgap

Abstract: A two-dimensional phononic crystal (PC) structure possessing a relatively low frequency range of complete bandgap is presented. The structure is composed of periodic spindle-shaped plumbum inclusions in a rubber matrix which forms a square lattice. The dispersion relation, transmission spectrum and displacement field are studied using the finite element method in conjunction with the Bloch theorem. Numerical results show that the present PC structure can achieve a large complete bandgap in a relatively low frequency range compared with two inclusions of different materials, which is useful in low-frequency noise and vibration control and can be designed as a low frequency acoustic filter and waveguides. Moreover, the transmission spectrum and effective mass are evaluated to validate the obtained band structure. It is interesting to see that within the band gap the effective mass becomes negative, resulting in an imaginary wave speed and wave exponential attenuation. Finally, sensitivity analysis of the effect of geometrical parameters of the presented PC structure on the lowest bandgap is performed to investigate the variations of the bandgap width and frequency.

Key words: phononic crystal, spindle-shaped inclusion, transmission spectrum, bandgap

中图分类号:  (Phonons in crystal lattices)

  • 63.20.-e
63.20.D- (Phonon states and bands, normal modes, and phonon dispersion) 62.30.+d (Mechanical and elastic waves; vibrations)