A linear model is developed for a hanging pipe aspirating fluid with internal flow velocity $U_i,$ flowing up the pipe from its lower end, and also subjected to an external flow of velocity $U_o$ flowing down from the upper end of the annulus formed between the pipe and a relatively shorter rigid outer tube; both the tube and pipe are cantilevered from their top ends. In this model, the pipe is modelled as an Euler–Bernoulli beam, with the internal flow modelled as a plug flow and the external one by means of slender-body theory; flow over the unconfined portion of the pipe is also taken into account. This model is discretized and solved using the Galerkin method to obtain the eigenfrequencies of the pipe for a number of flow velocity ratios $U_o/U_i$. In all cases, the pipe loses stability, mostly via first-mode flutter, at sufficiently high values of $U_i$. Subsequently, the theoretical results are compared with earlier theoretical results and also with all available experimental results. The present theoretical results are in reasonably good agreement with the experimental results.

The system under consideration represents an idealized mode of operation of ‘salt-mined caverns’, which are large underground storage spaces created to store hydrocarbons, such as natural gas and oil.

建立了具有内流速的悬管抽吸流体的线性模型${你}_{\mathrm{一世}},$ 从管道的下端向上流动，并受到外部速度流动的影响 ${你}_{○}$从管子和相对较短的刚性外管之间形成的环形空间的上端向下流动；管子和管道都从它们的顶端悬臂伸出。在这个模型中，管道被建模为欧拉-伯努利梁，内部流被建模为活塞流，外部流被建模为细长体理论；还考虑了管道非受限部分的流动。该模型使用 Galerkin 方法进行离散化和求解，以获得管道在多个流速比下的特征频率${你}_{○}/{你}_{\mathrm{一世}}$. 在所有情况下，管道失去稳定性，主要是通过第一模式颤振，在足够高的值${你}_{\mathrm{一世}}$. 随后，将理论结果与早期的理论结果以及所有可用的实验结果进行比较。目前的理论结果与实验结果相当吻合。

正在考虑的系统代表了“盐矿洞穴”的理想化操作模式，这是为储存碳氢化合物（如天然气和石油）而创建的大型地下存储空间。