中国物理B ›› 2007, Vol. 16 ›› Issue (4): 891-896.doi: 10.1088/1009-1963/16/4/003

• GENERAL • 上一篇    下一篇

Stability and vibration of a helical rod with circular cross section in a viscous medium

刘延柱, 盛立伟   

  1. Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, China
  • 收稿日期:2006-07-17 修回日期:2006-11-16 出版日期:2007-04-20 发布日期:2007-04-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10472067).

Stability and vibration of a helical rod with circular cross section in a viscous medium

Liu Yan-Zhu(刘延柱)† and Sheng Li-Wei(盛立伟)   

  1. Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, China
  • Received:2006-07-17 Revised:2006-11-16 Online:2007-04-20 Published:2007-04-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10472067).

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摘要： The stability and vibration of a thin elastic helical rod with circular cross section in a viscous medium are discussed. The dynamical equations of the rod in the viscous medium are established in the Frenet coordinates of the centreline with the Euler angles describing the attitudes of the cross section as variables. We have proved that the Lyapunov and Euler conditions of stability of a helical rod in the space domain are the necessary conditions for the asymptotic stability of the rod in the time domain. The free frequencies and damping coefficients of torsional and flexural vibrations of the helical rod in the viscous medium are calculated.

Abstract: The stability and vibration of a thin elastic helical rod with circular cross section in a viscous medium are discussed. The dynamical equations of the rod in the viscous medium are established in the Frenet coordinates of the centreline with the Euler angles describing the attitudes of the cross section as variables. We have proved that the Lyapunov and Euler conditions of stability of a helical rod in the space domain are the necessary conditions for the asymptotic stability of the rod in the time domain. The free frequencies and damping coefficients of torsional and flexural vibrations of the helical rod in the viscous medium are calculated.

Key words: thin elastic rod, viscous medium, torsional vibration, flexural vibration

中图分类号:  (Resonance, damping, and dynamic stability)

  • 46.40.Ff
46.70.Hg (Membranes, rods, and strings) 46.35.+z (Viscoelasticity, plasticity, viscoplasticity)