超临界输液管的振动特性及几类非线性现象探析

The flow of fluid through the pipe is typical of gyroscopic system because the pipe introduces a gyroscopic force. Due to this widespread application in many industry fields, the dynamic behavior of pipes conveying fluid has been the subject of several studies in current engineering problems encountered in hydroelectric and nuclear power plants, suction and pressure pipes, and fuel feeding lines in aerospace vehicles.As the flow velocity is incremented to a critical value, the undeformed configuration of the pipe becomes unstable and bifurcates into multiple equilibrium positions. The subject focuses on the vibration properties and several nonlinear phenomena of pipes conveying fluid in the supercritical regime. Conditions for the some internal resonances are established, and the condition implies that internal resonances are possible in the supercritical regime. The method of high order multiple scales is developed to present the solvability condition of approximate solutions. The modulation equations of the amplitude and the phase are derived from the condition. Asymptotic solutions and their stabilities are discussed. Some typical steady responses are determined via the amplitude-frequency curves. In addition to jumping, hysteresis and saturation, other dynamical behaviors are simulated to highlight the effects of the modal interaction in the internal resonance. On the other hand, the methods of simulating numerically study their dynamical characteristics. To investigate a way of internal resonance and nonlinearities terms in process of supercritical regime, which will contribute to the development of cross fields of fluids and strucutres.

输液管的振动是一个典型的陀螺系统，研究有着广阔的工程应用背景。当流速超过一定的临界值时，对于管径小于管道长度的细长直管，输液管的直平衡位形失稳，系统会重新稳定在曲线平衡位形。本项目以超临界条件下的输液管为研究背景，注重对宏观上输液管的曲线稳定位形进行振动分析和非线性现象的探析，来描述和预测输液管振动过程的力学行为。研究内容涉及超临界输液管的非线性数学模型，观测和计算出不同的内共振条件，特别是寻找非线性和内共振之间的关联。一方面，拟采用高阶多尺度近似解析方法求解控制方程，并判断解的稳定性，进而分析解的动态特性，探索出输液管的相关参数对解的各种影响；另一方面，通过对控制方程的数值模拟，研究超临界下管道的动力学特性，模拟跳跃、滞后、饱和等几类非线性现象的运动。探析超临界输液管的内共振和非线性现象之间的复杂的动力学行为，有助于理解和发展固液耦合振动问题。

当流速流速超过临界值，对于管径远远小于管道长度的细长支承直管，输液管的零平衡位形失稳，但是系统会重新稳定在非零平衡位形。这种平衡模式类似Euler杆屈曲行为。研究基于超临界流速范围内，通过动力学坐标变换后，管道控制方程变为带有变系数的偏微分-积分控制方程。利用解析方法和数值方法研究了输液管横向振动的非线性动力学特性，重点揭示了内共振条件下的复杂非线性的动力学现象。.在超临界条件下，对输液管横向受迫的控制方程进行非零平衡位形的坐标变换后，建立了受迫振动的扰动控制方程。对激励幅值量级的控制，可以分别研究系统的弱受迫和强受迫振动特性。采用Galerkin 截断与多尺度法相结合的方法， 考虑2:1内共振的条件下，研究管道受到弱受迫振动时发生前二阶主共振的非线性动力学现象。结果表明，这种典型的陀螺系统存在多种有趣的现象：双跳跃现象(Double-jumping)，软弹簧特性(Softening-spring)，硬弹簧特性(Hardening-spring)，滞后现象(Hysteresis)，饱和现象(Saturation)。同时，当流速在内共振附近逐渐变化时，首次演化出软弹簧特性变为硬弹簧特性的转变过程。.在超临界条件下，对输流管弱受迫扰动控制方程中的激励幅值量级上的扩大，可以实现强受迫振动。采用Galerkin 截断与多尺度法相结合的方法，考虑2:1内共振的条件下，研究管道受到强受迫振动时发生的次谐波共振、超谐波共振和组合共振时的非线性动力学现象。.在超临界条件下，对超临界输液管的弱受迫扰动模型进行四阶Galerkin 截断，利用陀螺系统的高维可解性理论，验证了二阶Galerkin 截断发现的内共振条件下的振动特性。同时证实高维陀螺系统的一般理论，具有普适性。.通过具体的数值算例，构造出超临界输液管横向振动的各种共振的频率响应曲线和幅值响应曲线，详细的讨论了各种参数，比如黏弹性系数、激励振幅、非线性系数以及超临界流速对共振响应曲线的影响，同时对响应曲线的稳定性进行了分析。最后，通过用数值求解的结果与解析获得的结果进行对比，证实了各种振动中出现的超临界非线性动力学现象。