中国物理B ›› 2007, Vol. 16 ›› Issue (4): 891-896.doi: 10.1088/1009-1963/16/4/003
刘延柱, 盛立伟
Liu Yan-Zhu(刘延柱)† and Sheng Li-Wei(盛立伟)
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.
中图分类号: (Resonance, damping, and dynamic stability)