Stability and modal evolution characteristics of pipe-in-pipe system with internal intermediate support

In this paper, the stability of the pipe-in-pipe (PIP) conveying fluid system with intermediate supports are studied. The focus of the study is mainly on the influence of the intermediate supports on the critical velocity boundary. The governing equations of the coupled system are established according to Hamilton's principle, and the modal functions in analytical solution form and the frequency equation in implicit function form are obtained by using the Laplace transform technique. In the numerical discussion part, the influence of the stiffness and position of the support on frequencies, modal functions, and critical flow velocity of the system is discussed. In the stability region diagrams of the cantilever PIP system, it is found that when the position and stiffness of the support change, the minimum critical flow velocity is frequently converted between different modes, and there are two different types of critical flow velocity conversion phenomena (CFVC). And high-order flutter instability, 'jump' phenomenon, S-shaped critical velocity boundary and modal conversion phenomenon are discussed in detail. In addition, the effective and negative regions of the support in the cantilever PIP and simply supported PIP systems are given.