基于非光滑理论的输流管非线性碰撞振动机理研究

Pipes conveying fluid are widely used in mechanical and nuclear engineering. The clearance between neighboring pipes or a pipe and constraints would lead to impacting vibration when the oscillation amplitude of the pipe becomes large enough. Such impacting vibration can result in failure of the pipe system and is an important topic in engineering applications and academic researches on the system of pipes conveying fluid. Previous studies on the impacting vibration of pipes conveying fluid are valuable but also have some insufficiency. The first inefficiency is that the smoothed impacting model, which cannot capture the strong non-linear phenomena during impacting process. The second one is the lack of a deep analysis on the non-planar vibrations of three-dimensional pipes with impacting force. This project is prepared to carry out the following three aspects: 1) Experimental researches on non-linear impacting dynamics of straight and curved pipes will be performed, aiming at developing a non-smooth description of the clearance impacting force and constructing a theoretical model for straight and curved pipes. 2) Exploring the impacting dynamics of pipes by introducing the cell-mapping method. The stability analysis is conducted when the pipe is restrained by single-point or distributed non-smooth constraints. The results will be compared with experiment data. 3) Experimental and theoretical analysis on the dynamics of straight and curved pipe bundles will be discussed, in order to reveal the mechanism of planar and non-planar vibrations and the exchange between these two types of vibrations. The findings of this project would enhance the understanding of the dynamics of impacting vibration of the dynamical system of pipes conveying fluid, broaden the research range of non-linear vibration, and provide theoretical foundation for explanation of abnormal phenomena of fluid-conveying pipes in engineering.

输流管是机械工程和核工程等领域广泛应用的工程结构，相邻管道之间或管道与部件之间的间隙会出现碰撞振动，可能导致结构失效或破坏，是工程界和学术界关注的重点问题。以往输流管的碰撞振动研究存在明显不足：采用光滑碰撞模型，无法捕获碰撞瞬间的强非线性现象；局限于管道的平面振动，非平面振动研究存在不足。本项目拟开展以下工作：1）完成直管和曲管的碰撞振动实验，分析实验数据提出管道与间隙碰撞的非光滑描述，并建立直管和曲管的非线性碰撞振动理论模型；2）引入胞映射方法对管道碰撞振动理论模型求解，研究在单点和分布非光滑约束下直管和曲管的碰撞振动特性，将结果与实验进行对比验证；3）建立直管束和曲管束的实验和理论碰撞振动模型，分析管道的平面和非平面振动，探索两种振动行为之间的转迁机制。本项目研究成果将加深人们对碰撞振动理论的理解，拓宽输流管非线性振动研究范围，为解释工程管道的异常现象提供理论支撑。

含间隙约束输流管的碰撞振动现象是核工业中热交换器设备经常出现的问题，结构发生碰撞的瞬间存在位移、速度、加速度甚至形状参数的突变，任何一个突变均会极大地影响系统动力学行为。目前，关于受间隙约束输流管的非线性碰撞振动过程中可能产生的非光滑现象及其机理的研究存在一定的不足，尤其是引入非光滑因素后输流管非线性动态响应特征随参数发展规律亟待进一步研究。本项目在前人已有工作的基础上，尝试从实验和理论层面探究具有间隙约束输流管的碰撞振动现象及其发展规律，主要研究内容有以下几个方面：建立了两端支承柔性输流管与刚性间隙约束的非线性模型，基于碰撞恢复系数推导了发生碰撞前后管道各部位状态向量的传递矩阵，通过数值方法得到了柔性管道与刚性约束之间的碰振动力学行为；建立了分段刚性管道与单侧刚性间隙约束的非线性模型，分析了刚性管与刚性约束之间“硬碰硬”的动力学现象，探讨了分岔路径随系统参数的变化规律；建立了立方非线性和修正的三线性间隙约束下两端支承管道在横向外流激励下的非线性动态响应，获得了管道分岔路径随轴向载荷和内流流速之间的变化规律；建立了柔性和刚性管道节段构成的刚柔耦合系统模型，通过分析系统的特征值问题获得了该刚柔耦合管道系统的稳定性流速区域随结构参数的变化规律；建立了三维悬臂输流管在脉动内流激励下的非线性模型，基于Floquet理论分析了相应线性模型的稳定性区域，并分析了该三维管道系统的动态响应随平均流速，脉动幅值和脉动频率之间的变化规律，以及受上述参数影响时的平面和非平面问题，为研究三维输流管系统与刚性间隙约束之间的非光滑动力学现象提供理论依据。本项目取得的研究成果有利于拓展输流管动力学的研究范围，促进输流管非线性动力学的发展。