Direct calculation of limit cycles of draw resonance and their stability in spinning process
Direct calculation of limit cycles of draw resonance and their stability in spinning process
复制标题
纺丝过程中牵伸共振极限环的直接计算及其稳定性
DOI：
10.1678/rheology.36.133
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发表时间：
2008
影响因子：
1.3
通讯作者：
J. Hyun
中科院分区：
文献类型：
--
作者：
J. Yun;D. Shin;J. Lee;H. Jung;J. Hyun
绘制共振，已知控制的开始不稳定发生在拉伸为主的聚合物过程中，已经研究了使用分岔分析方法。利用牛顿法实现伪弧长延拓格式，直接得到了沿起始点或Hopf点上的降噪比的抽吸共振时周期轨迹。在振荡的一个周期内，用时间积分法计算了用于确定极限环稳定性的单矩阵的Floquet乘子。结果表明，无论对牛顿流体还是粘弹性流体，当降速比增大时，其极限环在起始点上都更加稳定，因此，降速共振是一种稳定的超临界Hopf分岔。
Draw resonance, known to govern the onset of instability occurring in extension-dominant polymer processes, has been investigated using the bifurcation analysis method. Time-periodic trajectories of draw resonance along the drawdown ratio over the onset point or Hopf point, have been directly obtained by Newton's method implemented with pseudo arc-length continuation scheme. Floquet multipliers of the monodromy matrix to determine the stability of limit cycles have been also computed by time-integration during one period of the oscillation. It has been revealed that the limit cycles over the onset are more stable when drawdown ratio rises for both Newtonian and viscoelastic fluids, so draw resonance is a stable supercritical Hopf bifurcation.