摘要
讨论圆截面弹性细杆在黏性介质中的平面振动.基于Kirchhoff理论,以杆中心线的Frenet坐标系为参考系,建立其动力学方程,杆中心线为任意平面曲线时,其扭转振动与弯曲振动解耦.讨论两端固定条件下任意形状杆的平面扭转振动,以及无扭转的轴向受压直杆和圆环杆的平面弯曲振动,导出其自由振动频率和阻尼系数.证明空间域内压杆的Lyapunov稳定性和欧拉稳定性条件为时域内渐近稳定性的充分必要条件,或无阻尼压杆的稳定性必要条件.圆环杆平衡恒满足渐近稳定性条件.
The planar vibration of a thin elastic rod with circular cross section in viscous medium is discussed. Based on the Kirchhoff＇s theory the dynamical equations of the rod are established in the Frenet coordinates of the centerline. The torsional vibration is decoupled from the flexural vibration when the centerline is an arbitrary planar curve. The planar torsional vibration of an arbitrary planar rod and the planar flexural vibrations of an axially compressed straight rod and a ring without torsion are discussed when the ends of the rod are fixed. The natural frequencies and the damping coefficients are derived. It is proved that the Lyapunov＇s and Euler＇s conditions of stability of an axially compressed straight rod in the space domain are the sufficient and necessary condition of asymptotic stability of the rod in the time domain, or the necessary condition of stability of the rod without damping. The asymptotic stability of a ring in viscous medium is always satisfied.
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2005年第11期4989-4993,共5页
Acta Physica Sinica
基金
国家自然科学基金(批准号:10472067)资助的课题.~~
