中国物理B ›› 2005, Vol. 14 ›› Issue (8): 1501-1506.doi: 10.1088/1009-1963/14/8/004

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Doubly coupled vibration band gaps in periodic thin-walled open cross-section beams

郁殿龙, 刘耀宗, 邱静, 王刚, 温激鸿   

  1. Institute of Mechatronical Engineering, National University of Defense Technology, Changsha 410073, China; PBG Research Center, National University of Defense Technology, Changsha 410073, China
  • 收稿日期:2005-01-12 修回日期:2005-02-28 出版日期:2005-07-13 发布日期:2005-07-13
  • 基金资助:
    Project supported by the 973 State Key Development Program for Basic Research of China (Grant No 51307).

Doubly coupled vibration band gaps in periodic thin-walled open cross-section beams

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

  1. Institute of Mechatronical Engineering, National University of Defense Technology, Changsha 410073, China; PBG Research Center, National University of Defense Technology, Changsha 410073, China
  • Received:2005-01-12 Revised:2005-02-28 Online:2005-07-13 Published:2005-07-13
  • Supported by:
    Project supported by the 973 State Key Development Program for Basic Research of China (Grant No 51307).

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摘要： This paper studies flexural-torsional doubly coupled vibration through periodic thin-walled open cross-section beams composed of two kinds of materials.Based on the doubly coupled vibration equation, plane wave expansion method for the thin-walled beams is provided. If the filling fraction keeps constant, the lattice is one of the factors that affect the normalized gap width. If the lattice and filling fraction keeps constant, the Young modulus contrast plays a fundamental role for the band gap width, but not density contrast. Finally, the frequency response of a finite periodic binary beam is simulated by finite element method, which provides an attenuation of about 40dB in the frequency range of the band gaps. The findings will be significant in the application of phononic crystals.

关键词: phononic crystals, doubly coupled vibration, band gaps, thin-walled beam

Abstract: This paper studies flexural-torsional doubly coupled vibration through periodic thin-walled open cross-section beams composed of two kinds of materials.Based on the doubly coupled vibration equation, plane wave expansion method for the thin-walled beams is provided. If the filling fraction keeps constant, the lattice is one of the factors that affect the normalized gap width. If the lattice and filling fraction keeps constant, the Young modulus contrast plays a fundamental role for the band gap width, but not density contrast. Finally, the frequency response of a finite periodic binary beam is simulated by finite element method, which provides an attenuation of about 40dB in the frequency range of the band gaps. The findings will be significant in the application of phononic crystals.

Key words: phononic crystals, doubly coupled vibration, band gaps, thin-walled beam

中图分类号:  (Electron density of states and band structure of crystalline solids)

  • 71.20.-b
63.20.-e (Phonons in crystal lattices) 02.70.Dh (Finite-element and Galerkin methods) 46.40.-f (Vibrations and mechanical waves) 46.70.De (Beams, plates, and shells)