摘要
基于得到的水平悬臂输液管非线性动力学控制方程,详细研究了由流速最小临界值诱发的3∶1内共振.通过观察内共振调谐参数、主共振调谐参数和外激励幅值的变化,发现在内共振临界流速附近,流速导致系统出现模态转换、鞍结分岔、Hopf分岔、余维2分岔和倍周期分岔等非线性动力学行为,对应的管道系统的周期运动失稳出现跳跃、颤振和更加复杂的动力学行为.通过理论结果与数值模拟比较,表明了理论分析的有效性和正确性.
The Newtonian method is employed to obtain nonlinear mathematical model of motion of a horizontally cantilevered and inflexible pipe conveying fluid, The Order magnitudes of relevant physical parameters are analyzed qualitatively to establish a foundation on the fuither study of the model. The method of multiple scales is used to obtain eigenfunctions of the linear flee-vibration modes of the pipe. The boundary conditions yield the characteristic equations from which eigenvalues can be derived. It is found that flow velocity in the pipe may induced the 3：1, 2： 1 and 1 ： 1 internal resonances between the first and second modes such that the mechanism of flow-induced internal resonances in the pipe under consideration is explained theoretically. The 3：1 internal resonance first occurs in the system and is, thus, the most important since it corresponds to the minimum critical velocity.
出处
《应用数学和力学》
CSCD
北大核心
2006年第7期819-824,共6页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(10472083)
国家自然科学基金(重点)资助项目(10532050)
关键词
输液管
内共振
稳定性
分岔
pipe conveying fluid
internal resonance
stability
bifurcation
