Unstable oscillation of tubular cantilevers conveying fluid I. Theory
Unstable oscillation of tubular cantilevers conveying fluid I. Theory
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DOI：
10.1098/rspa.1966.0187
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发表时间：
1966-08
期刊：
影响因子：
--
通讯作者：
R. W. Gregory;M. Païdoussis
中科院分区：
文献类型：
--
作者：
R. W. Gregory;M. Païdoussis
当上游端固定而另一端自由的管内流体流速超过某一临界值时，系统就会变得不稳定，小的随机扰动就会发展成大振幅的横向振荡。本文讨论了在水平面上运动的系统的稳定性条件。忽略管内材料的内摩擦和周围流体的影响，构造了对应于中性稳定性条件的通用稳定性曲线，从而分离了稳定和不稳定的区域。这是通过精确方法和近似地将运动表示为悬臂梁的前几个本征函数之和来求解运动方程。在两个有代表性的情况下，连续增加的流速值，以证明如何从稳定过渡到不稳定的系统的四个最低模式的复杂频率进行计算。
When the velocity of fluid flow in a tube, fixed at the upstream end and free at the other, is increased beyond a certain critical value, the system becomes unstable and small random perturbations grow into lateral oscillations of large amplitude. This paper is concerned with establishing the conditions of stability in the case of a system which is constrained to move in a horizontal plane. Neglecting internal friction in the material of the tube and the effect of the surrounding fluid, a universal stability curve is constructed corresponding to conditions of neutral stability and hence separating stable and unstable régimes. This is done by finding solutions to the equations of motion both by exact methods and also approximately by expressing the motion as the sum of the first few eigenfunctions of a cantilever beam. The complex frequency of the four lowest modes of the system is calculated in two representative cases for successively increasing values of the flow velocity to demonstrate how transition from stability to instability takes place.