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

• 来源期刊: 中国物理（英文版）
• 关键词: thin elastic rod viscous medium torsional vibration flexural vibration
• 年，卷（期）: 2007,（4）
• 页码范围: 891-896
• 页数: 6页
• 语种: 英文

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.