On the dynamics of curved pipes transporting fluid. Part I: Inextensible theory

This paper treats the dynamics and stability of curved pipes conveying fluid. The cases of pipes supported at both ends, as well as cantilevered pipes, are considered. A “modified” inextensible theory is developed, which retains the assumption of inextensibility of the centreline of the pipe as in the “conventional” inextensible theory, but the steady-state initial forces due to the centrifugal and pressure forces are nevertheless taken into account. The problem is solved via a finite-element formulation. The behaviour of curved pipes with supported ends according to the new theory is similar to that predicted by the extensible theories, i.e., the system does not lose stability as the flow velocity is increased, for either in-plane or out-of-plane motions; however, the new theory involves much less computational effort. For cantilevered pipes, the theory predicts a smaller critical flow velocity, as compared to the “conventional” inextensible theory. It is also observed that viscosity of the fluid has no effect on the dynamics, similarly to the case of straight pipes conveying fluid.