中国物理B ›› 2009, Vol. 18 ›› Issue (4): 1316-1321.doi: 10.1088/1674-1056/18/4/004

• GENERAL • 上一篇    下一篇

Coupled flexural-torsional vibration band gap in periodic beam including warping effect

方剑宇, 郁殿龙, 韩小云, 蔡力   

  1. Institute of Mechatronical Engineering, and PBG Research Center, National University of Defense Technology, Changsha 410073, China
  • 收稿日期:2008-08-16 修回日期:2008-11-13 出版日期:2009-04-20 发布日期:2009-04-20
  • 基金资助:
    Project supported by the State Key Development Program for Basic Research of China (Grant No 51307) and the National Natural Science Foundation of China (Grant No 50575222).

Coupled flexural-torsional vibration band gap in periodic beam including warping effect

Fang Jian-Yu(方剑宇)†, Yu Dian-Long(郁殿龙), Han Xiao-Yun(韩小云), and Cai Li(蔡力)   

  1. Institute of Mechatronical Engineering, and PBG Research Center, National University of Defense Technology, Changsha 410073, China
  • Received:2008-08-16 Revised:2008-11-13 Online:2009-04-20 Published:2009-04-20
  • Supported by:
    Project supported by the State Key Development Program for Basic Research of China (Grant No 51307) and the National Natural Science Foundation of China (Grant No 50575222).

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摘要： The propagation of coupled flexural-torsional vibration in the periodic beam including warping effect is investigated with the transfer matrix theory. The band structures of the periodic beam, both including warping effect and ignoring warping effect, are obtained. The frequency response function of the finite periodic beams is simulated with finite element method, which shows large vibration attenuation in the frequency range of the gap as expected. The effect of warping stiffness on the band structure is studied and it is concluded that substantial error can be produced in high frequency range if the effect is ignored. The result including warping effect agrees quite well with the simulated result.

Abstract: The propagation of coupled flexural-torsional vibration in the periodic beam including warping effect is investigated with the transfer matrix theory. The band structures of the periodic beam, both including warping effect and ignoring warping effect, are obtained. The frequency response function of the finite periodic beams is simulated with finite element method, which shows large vibration attenuation in the frequency range of the gap as expected. The effect of warping stiffness on the band structure is studied and it is concluded that substantial error can be produced in high frequency range if the effect is ignored. The result including warping effect agrees quite well with the simulated result.

Key words: phononic crystals, coupled flexural-torsional beam, transfer matrix method, warping stiffness

中图分类号:  (Vibrations and mechanical waves)

  • 46.40.-f
46.70.De (Beams, plates, and shells) 71.20.Be (Transition metals and alloys)