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.
Received: 17 July 2006
Revised: 16 November 2006
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10472067).
Cite this article:
Liu Yan-Zhu(刘延柱) and Sheng Li-Wei(盛立伟) Stability and vibration of a helical rod with circular cross section in a viscous medium 2007 Chinese Physics 16 891
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