## 留言板

 引用本文: 张博，史天姿，张贻林，孙东生，袁从敏，丁虎，陈立群. 旋转输液管动力稳定性理论分析 [J]. 应用数学和力学，2022，43（2）：166-175
ZHANG Bo, SHI Tianzi, ZHANG Yilin, SUN Dongsheng, YUAN Congmin, DING Hu, CHEN Liqun. Theoretical Analysis on Dynamic Stability of Rotating Pipes Conveying Fluid[J]. Applied Mathematics and Mechanics, 2022, 43(2): 166-175. doi: 10.21656/1000-0887.420135
 Citation: ZHANG Bo, SHI Tianzi, ZHANG Yilin, SUN Dongsheng, YUAN Congmin, DING Hu, CHEN Liqun. Theoretical Analysis on Dynamic Stability of Rotating Pipes Conveying Fluid[J]. Applied Mathematics and Mechanics, 2022, 43(2): 166-175.

• 中图分类号: O32

## Theoretical Analysis on Dynamic Stability of Rotating Pipes Conveying Fluid

• 摘要:

基于Lagrange原理和假设模态法建立了旋转输液管的动力学模型。通过降阶升维的方法求解系统的特征值问题，并分析了旋转输液管自由振动特性。得到了不同端部集中质量和转速下，系统特征值随流速升高的演变轨迹。揭示了临界流速随系统参数的变化规律。研究发现，内部流体的流动对旋转输液管动力学特性存在显著影响。在某些参数组合下，系统低阶模态能够形成不同形式的内共振关系。预示了旋转输液管模型蕴含丰富的动力学现象。

• 图  1  旋转输液管动力学模型

Figure  1.  The sketch for a rotating pipe conveying fluid

图  2  不同试探函数个数下前三阶特征根轨迹曲线 (Tm* = 0，Ω* = 0)：(a) N1 = N2 = 5；(b) N1 = N2 = 8；(c) N1 = N2 = 10；(d) N1 = N2 = 12

Figure  2.  The trajectories of the 1st 3 eigenvalues for different trail function numbers (Tm* = 0, Ω* = 0): (a) N1 = N2 = 5; (b) N1 = N2 = 8; (c) N1 = N2 = 10; (d) N1 = N2 = 12

图  3  转速对特征根轨迹的影响 (Tm* = 0)：(a) Ω* = 4；(b) Ω* = 8；(c) Ω* = 12

Figure  3.  Effects of the rotating speed on the eigenvalue trajectories (Tm* = 0): (a) Ω* = 4; (b) Ω* = 8; (c) Ω* = 12

4  端部集中质量对特征根轨迹的影响 (Ω* = 4)：(a) Tm* = 0.2；(b) Tm* = 0.4；(c) Tm* = 0.6

4.  Effects of the tip mass on the eigenvalue trajectories (Ω* = 4): (a) Tm* = 0.2; (b) Tm* = 0.4; (c) Tm* = 0.6

图  5  不同端部集中质量下临界流速随转速的变化规律 (Ω* = 4)

Figure  5.  Variations of the critical fluid velocity with the rotating speed for different tip masses (Ω* = 4)

图  6  矩阵CG对系统第一阶固有频率的影响 (Ω* = 4，Tm* = 0.2)

Figure  6.  The effects of matrices C and G on the system 1st natural frequency (Ω* = 4, Tm* = 0.2)

图  7  旋转输液管前三阶固有频率随流体流速的变化规律 (Ω* = 2，Tm* = 0.2)

Figure  7.  The variations of the 1st 3 natural frequencies of the rotating pipe (Ω* = 2, Tm* = 0.2)

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##### 出版历程
• 收稿日期:  2021-06-17
• 录用日期:  2021-06-17
• 修回日期:  2021-07-03
• 网络出版日期:  2021-12-30
• 刊出日期:  2022-02-01

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