Abstract In this paper, the instability and three-dimensional (3-D) nonlinear dynamics of a supported pipe subjected concurrently to internal and external axial flows are investigated, for the flow velocity of internal fluid being either steady or pulsatile. For that purpose, a 3-D version of nonlinear governing equations for two perpendicular lateral displacements of the pipe are derived by the use of extended Hamilton's principle. Unlike previous two-dimensional (2-D) versions of governing equation for a supported pipe subjected concurrently to external and internal axial flows, this new 3-D version of governing equations is capable of predicting the non-planar motions of the pipe. Based on linear analyses, it is shown that buckling instability may occur for an internal steady fluid flow while parametric instability can be generated by an internal pulsatile flow. In the nonlinear analyses, the nonlinear dynamics of the pipe with various internal and external flow velocities for different pulsating frequencies and amplitudes are represented by means of bifurcation diagrams, time traces, phase portraits, oscillation trajectories, power spectral density (PSD) diagrams and Poincare maps. Some interesting dynamical behaviors, including periodic, quasi-periodic and chaotic motions, are detected in a wide range of pulsating frequency of interest. In many cases, non-planar motions of the pipe may be induced by fluid flows. These non-planar motions, however, need to be determined by using the present 3-D theoretical model instead of previously used 2-D ones for supported pipes subjected concurrently to internal and external axial flows.

中文翻译：

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同时受外轴流作用的流体输送管三维动力学

摘要 本文研究了同时受到内部和外部轴向流作用的支撑管的不稳定性和三维 (3-D) 非线性动力学，因为内部流体的流速是稳定的还是脉动的。为此，管道的两个垂直横向位移的非线性控制方程的 3-D 版本是通过使用扩展的哈密顿原理推导出来的。与先前二维 (2-D) 版本的受支撑管道同时受到外部和内部轴流影响的控制方程不同，这个新的 3-D 版本控制方程能够预测管道的非平面运动。基于线性分析，结果表明，内部稳定流体流动可能会发生屈曲不稳定，而内部脉动流动可能会产生参数不稳定。在非线性分析中，通过分叉图、时间轨迹、相图、振荡轨迹、功率谱密度 (PSD) 图和 Poincare 来表示管道在不同脉动频率和振幅下具有各种内部和外部流速的非线性动力学地图。在广泛的感兴趣的脉动频率范围内检测到一些有趣的动力学行为，包括周期性、准周期性和混沌运动。在许多情况下，流体流动可能会引起管道的非平面运动。然而，这些非平面运动，