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首页> 外文会议>ASME(American Society of Mechanical Engineers) Pressure Vessels and Piping Conference 2006 vol.4 pt.A: Fluid-Structure Interaction >THE BEHAVIOUR OF FLUID-CONVEYING PIPES, SUPPORTED AT BOTH ENDS, BY THE COMPLETE EXTENSIBLE NONLINEAR EQUATIONS OF MOTION
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THE BEHAVIOUR OF FLUID-CONVEYING PIPES, SUPPORTED AT BOTH ENDS, BY THE COMPLETE EXTENSIBLE NONLINEAR EQUATIONS OF MOTION

机译：完全可扩展的非线性运动方程在两端都支持的输液管道的行为

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摘要

In this paper, the post-divergence behaviour of fluid-conveying pipes supported at both ends is studied using the complete extensible nonlinear equations of motion. The two coupled nonlinear partial differential equations are discretized via Galerkin's method and the resulting set of ordinary differential equations is solved by Houbolt's finite difference method and also using AUTO. Typically, the pipe is stable and retains its original static equilibrium position up to where it loses stability by a supercritical pitchfork bifurcation. By increasing the flow velocity, the amplitude of the buckled position increases, but no secondary instability can be observed thereafter, in agreement with Holmes' results for his simplified model. The effect of different parameters on the behaviour of the pipe has been studied. By increasing the externally applied tension, or by increasing the gravity parameter, the critical flow velocity for the pitchfork bifurcation increases. The pitchfork bifurcation is subcritical if the nondimensional externally imposed tension, is greater than the nondimensional axial rigidity. The solution in the vicinity of the critical point for this case is confirmed to be subcritical, although the fold and the stable non-trivial solution thereafter could not be seen — perhaps because the model is correct to only third-order of magnitude. Dynamic instabilities may be possible for a pipe hinged at both ends but free to slide axially at the downstream end, according to preliminary results.
机译：在本文中，使用完整的可扩展非线性运动方程研究了两端支撑的输液管的后扩散行为。通过Galerkin方法离散化两个耦合的非线性偏微分方程，并通过Houbolt的有限差分法和AUTO求解所得的一组常微分方程。通常，管道是稳定的，并保持其原始的静态平衡位置，直到由于超临界干草叉分叉而使其失去稳定性为止。通过增加流速，弯曲位置的幅度增加，但是此后未观察到二次不稳定性，这与Holmes简化模型的结果一致。研究了不同参数对管道性能的影响。通过增加外部施加的张力，或通过增加重力参数，干草叉分叉的临界流速增加。如果无量纲的外部施加的拉力大于无量纲的轴向刚度，则干草叉分叉为亚临界。尽管此后无法看到折痕和稳定的平凡解，但仍确认此情况下临界点附近的解是次临界的-也许是因为模型仅对三阶量值是正确的。根据初步结果，两端铰接但在下游端轴向自由滑动的管道可能会出现动态不稳定性。

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