## 留言板

 引用本文: 黄慧春, 张艳雷, 陈立群. 受迫振动的超临界输液管Galerkin数值模拟[J]. 应用数学和力学, 2014, 35(10): 1100-1106.
HUANG Hui-chun, ZHANG Yan-lei, CHEN Li-qun. A Galerkin Numerical Method for the Pipe Conveying Supercritical Fluid Under Forced Vibration[J]. Applied Mathematics and Mechanics, 2014, 35(10): 1100-1106. doi: 10.3879/j.issn.1000-0887.2014.10.004
 Citation: HUANG Hui-chun, ZHANG Yan-lei, CHEN Li-qun. A Galerkin Numerical Method for the Pipe Conveying Supercritical Fluid Under Forced Vibration[J]. Applied Mathematics and Mechanics, 2014, 35(10): 1100-1106.

• 中图分类号: O322

## A Galerkin Numerical Method for the Pipe Conveying Supercritical Fluid Under Forced Vibration

Funds: The National Natural Science Foundation of China(11302122)
• 摘要: 当流速超过临界值，输液管的直线平衡位形会发生失稳，但是系统会重新稳定在新的曲线平衡位置.通过引入坐标变换的方法，动力学模型转变为含有变系数的偏微分控制方程.采用4阶Galerkin截断的方法，使控制方程转变为常微分方程.给出具体的数值算例，发现4阶截断的固有频率要比2阶截断的固有频率更精确.同时，计算出前两阶固有频率出现可公度的情况，从而激发2∶1内共振现象.利用Runge-Kutta数值模拟的方法，在发生内共振流速范围的特定区域进行大量数值运算，结果表明高维系统的条件下，管道的不同径向坐标点的横向位置处，均出现软硬特性，而在内外共振完全调谐时，出现双跳跃现象.
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##### 出版历程
• 收稿日期:  2014-04-22
• 修回日期:  2014-09-10
• 刊出日期:  2014-10-15

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