纤维增强功能梯度输流管道振动的非线性行为研究

In view of the fact that the fiber reinforced composite materials are widely used for the pipes conveying fluid in engineering, different from the previous pipes, the dynamic behaviors induced by non-uniformity and anisotropy of materials may exhibit more complicated. This project is dedicated to study nonlinear vibration behaviors of the fiber reinforced functionally graded pipes conveying fluid, the research contents include that the mathematical model of the fluid-conveying pipes with some general boundary conditions and subjected to excitations is established by considering the materials properties of multi-directional functionally graded distributions and the geometric nonlinearity in the piping plane. Semi-analytical and numerical methods will be utilized to solve the natural frequencies and modes for the linear vibration. The stabilities of the system under the conditions of the steady flow and parametric resonance are respectively analyzed. Then, based on the obtained linear results, the solutions of the nonlinear vibration would be found using some approximate analytical techniques. The numerical and experimental methods are used to verify the accuracy of the theoretical analysis. Through mainly investigating the mechanism of fluid–solid interaction of the pipes, the instability rule will be established. The possible stability enhancement by tuning fiber direction angle, fiber arrangement rule and functionally graded indexes will be discussed. In addition, the principal resonance, internal resonance and bifurcation characteristics will be explored. The nonlinear dynamic evolution of fiber reinforced pipes conveying fluid will be revealed. This research will provide technical reserve for the design and manufacture in engineering. Moreover, the present work also show us a new theoretical basis to perform study on infinite dimensional gyro and dynamic system with nonlinearity.

在工程中纤维增强复合材料被广泛应用于传输流体管道，区别于传统的管道，材料的非均匀和各向异性将会引起系统更加复杂的动力学行为。本项目致力于纤维增强功能梯度输流管道振动的非线性行为研究，研究内容包括考虑纤维增强材料属性沿管道平面多方向功能梯度分布和几何非线性，建立几类约束和载荷作用下输流管道的数学模型，用半解析半数值法求解线性派生系统的固有特性；分析系统在定常流和参数共振情况下的稳定性；并以此为基础用近似解析方法研究系统的非线性振动解；利用数值和实验方法验证理论分析正确性。通过重点研究系统的流固耦合机理，建立失稳判定准则，讨论纤维方向角、纤维排列规律和功能梯度指数对改善系统稳定性的可能性，以及探究系统主共振、耦合内共振及分岔特性，揭示纤维增强输流管道的复杂非线性动力学演化规律，为工程设计和制造提供技术储备，同时也为无限维陀螺非线性动力系统的研究提供新的理论依据。

从广泛存在于工程中纤维增强复合材料构造的传输流体管道的动力学实际问题出发，基于非线性动力学、流体力学和弹性力学理论，本项目致力于纤维增强功能梯度输流管道振动的非线性行为研究，主要研究内容和成果如下：建立几类约束和载荷作用下纤维增强多方向功能梯度输流管道的动力学模型，提出了Galerkin迭代方法寻找三维功能梯度梁类结构非线性弯曲模态闭式解，微分求积方法验证了所提出解析解正确性；研究了输流管道参数振动的稳定性和非线性参数振动响应；研究了复杂约束三维功能梯度输流管道的减振和能量采集一体化设计，通过 Galerkin 截断及谐波平衡+时频交换技术对系统主共振周期解进行追踪，揭示了输流管道的复杂非线性动力学演化规律，得到了整合设计提高减振和能量采集效果的机理，即较低的轴向功能梯度指数和较高的径向和周向功能梯度指数使所提出的系统更容易通过 NS 分岔生成泡状响应，进而明显地增强响应峰值；提出了主被动混合压电网络对输流管道振动进行控制，解决了传动被动控制方法的低频区域失效和频带过窄的问题。通过三年的努力，完成了全部研究计划，发表SCI论文21篇。本项目研究成果可为液体火箭防纵向耦合振动（Pogo）的设计等工程领域提供技术储备，同时也为无限维陀螺非线性动力系统的研究提供新的理论依据。