###### Abstract
In [6], [PERSON] and [PERSON] studied various aspects of the dynamic characteristic of clusters of tubular pipes which were  
Figure 1: Schematic view of the pipe configuration. A hanging flexible cantilevered pipe conveying fluid is partially confined inside a shorter inflexible external pipe. (**a**) the system considered in this paper; (**b**) the system considered in [1]. subjected to internal flows and concurrently surrounded by bounded outer axial flows. To establish general characteristics of free motions, they obtained the eigenfrequencies of the system and studied their evolution by increasing either external or internal flows. In [PERSON] and [PERSON] (2016), [PERSON] and [PERSON] established a mathematical model to investigate the vibration and stability of a submerged and inclined concentric pipe system which subjected to internal and external flow, and obtained the resonant frequencies of the system. In [PERSON] and [PERSON] (2016), [PERSON] et al. developed a theoretical model to study the vibration of a hanging tubular cantilever which was centrally inside a cylindrical container, with fluid flowing within the cantilever, and discharging from the free end. The configuration thus resembles that of a drill-string with a floating fluid-powered drill-bit. Of particular interest is the study in [PERSON] and [PERSON] preliminarily discussed the dynamics of the pipe configuration shown in Figure 1b. Furthermore, they developed a theoretical model and carried out corresponding experiments. Because the length of the cantilevered pipe system in practical applications is on the order of one kilometer, how the system behavior evolves is of interest as the length increases. Theoretical and experimental studies [PERSON] and [PERSON] (2016); [PERSON] and [PERSON] (2016) regarding long hanging vertical pipes conveying fluid have shown that both the critical flow velocity and associated frequency for instability tend to be asymptotic toward different limiting values with increasing the length of the pipes. The literature related to aspirating cantilevered pipes was believed to be useful for analyzing the dynamics of a vertical hanging pipe shown in Figure 1a. For example, in [PERSON] and [PERSON] (2016); [PERSON] and [PERSON] (2016), the authors theoretically and experimentally considered the dynamic stability of a submerged cantilever pipe aspirating fluid, which could be applied in deep ocean mining. Figure 2: Schematic view of the salt cavern underground energy storage application. Fresh water or light brine is injected into the inner tubing, and high-concentration brine is expelled through the annular space in between the inner and outer tubings. This process is known as direct circulation, as distinguished from reverse circulation. Direct and reverse circulations are alternately employed until the salt cavern achieves the design shape and dimensions. Several key dimensions of the system under consideration are defined in Figure 1a. The \(x\)-axis lies in the undeflected centerline of the internal cantilever pipe, while the \(z\)-axis lies along the lateral direction and is perpendicular to the \(x\)-axis. \(L\) is the length of the cantilever pipe, while \(L_{s}\) is the length of the shorter inflexible external pipe (i.e. the length of the annular passage). \(U_{i}\) is the internal flow velocity (area average flow velocity) inside the cantilevered pipe, and \(U_{o}\) is the external flow velocity (area average flow velocity) in the annular passage with reference to the cantilever pipe. Firstly, the present paper studies the linear idealized system shown in Figure 1a. We present a derivation of a theoretical model as well as a method of solving it are discussed. Secondly, we give theoretical results for slender leaching-tubing-like systems which are associated with the industrial application of salt cavern storage. We also obtained some unexpected and interesting results by numerical simulation. Finally, we present general conclusions.