大变形输液管的非线性、非平面振动研究

Flow-induced vibration of pipes conveying fluid has always been one of the hot researches in the fluid-solid interaction dynamics field. However，there are still some kinds of flexible pipes，such as the hose in aerial refueling system and offshore oil pipe and etc., needing further investigation. Characteristics of these flexible pipe systems are of large deformation, and coupling of in-plane and out-plane vibration (i.e. the non-planar vibration). There are several difficulties in the research (i.e. our research focus of this Fund): 1. Four governing equations (two for transversal displacement; one for axial displacement; one for rotation) are required; 2. In order to develop the more sophisticated motion equations, the second Piola-Kirchhoff stress and the Green-Lagrange strain tensors should be adopted to describe the stress and strain of the large deformation pipe. Obviously, the complexity to set up this new dynamic model is much more than those of in-plane vibration; 3. How to solve it? The Absolute Nodal Coordinate Formulation (ANCF), which is very popular recently, will be adopted to solve the problem. The author’s expectation, the mechanical behaviors of the pipe system revealed in this research will be richer and more diverse than those of in-plane vibration of traditional straight/curved pipe conveying fluid. Therefore, the numerical identification of complicated nonlinear dynamic response of the pipe system and experimental tests are also key points in this research. So, this project is a further and deeper investigation in the field of flow-induced vibrations of pipes conveying fluid, and has significant values in theory and application.

输液管的流致振动一直是流固耦合动力学研究的热点之一。但有些形式的柔性管路（如飞机空中加油的管路、海洋中的采油管等）的研究还有待深入，这类管路的特点是大变形、面内和面外运动（即非平面振动）的耦合。对该问题的研究有几个难点（亦即本申请拟研究的重点）：一是控制方程的数目需要4个（2个横向位移、1个轴向位移、1个扭转角）；二是需采用Green应变张量和第二Piola Kirchhoff应力张量来描述大变形管的应变和应力，以建立更完善的运动方程；其复杂程度远大于管的面内振动；三是如何求解？最近兴起的 “绝对节点坐标法”（ANCF）将用于本问题的求解，笔者预期：本研究所揭示管的力学行为应该比输液管/曲管面内振动的更丰富、更多彩，因此对输液管非线性复杂动力响应的数值识别、实验测试也是本研究的关键。总之，本项目是输液管流致振动研究的进一步深入，具有重要的理论和应用价值。

本项目的主要研究工作与成果有：（1）长度随时间变化的输液管之非线性动力分析。发现输流管伸长速率显著降低了颤振失稳的临界流速，且临界流速值随管伸长速率的增加而减小；（2）在液体中轴向运动的杆（梁）之动力分析。该研究引入一个“轴向附加质量参数”来修正梁振动时所黏附的流体质量，同时给出了流体作用在梁（有横向变形和轴向运动）上的非线性作用力，成功实现建模及求解分析，这也许是业内较新的研究工作；（3）碰撞约束下输液管的非线性振动。发现在平行板约束下, 管道发生非平面颤振失稳后, 在较小流速范围内出现空间周期和概周期运动, 当流速达到一定值时, 该空间运动会过渡到平面周期运动, 且不同的流速对应的平面运动的方位也有所不同；（4）轴向基础激励下输液管的平面与非平面振动。发现流速、激励频率和激励幅值对该管道的稳定区域有较大影响，且在一定的轴向基础激励频率范围内，自激非平面振动可以演化为平面振动等现象；（5）轴向外流作用下输液管的非线性振动。其研究成果将有助于水下仿生机器人的设计；（6）基于绝对节点坐标法分析初始微弯（一种初始缺陷）大变形输液管的非线性振动。发现该管颤振失稳的临界流速可能比直管略低或大大高于直管，这主要取决于管初始微弯的形状和程度；（7）申请了一发明专利《一种基于流致振动驱动的水下仿生蝌蚪》并有望进行成果转化，在水下仿生机器人设计与制作方法上有所创新与应用。总之，感谢国家的基金支持，才有这些丰富的研究结果并有望应用于核电、水下机器人、深海采油及飞机空中加油等多个领域，也使输液管的流致振动研究达到一个新的深度和广度。另外，本项目在人才培养方面也有硕果，团队里有3名博士毕业、1名成为国家科协的“托举”人才。

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