Dynamic stability of pipes conveying fluid

This paper deals with the dynamics and stability of flexible pipes containing flowing fluid, where the flow velocity is either entirely constant, or with a small harmonic component superposed. An extensive historical review of the subject is given. In the case of constant flow velocity, the dynamics of the system is examined in a general way and it is shown that conservative systems are subject not only to buckling (divergence) at sufficiently high flow velocities, but also to oscillatory instabilities (flutter) at higher flow velocities. Also presented are some new results for cases of systems subjected to internal dissipative forces. In the case of harmonically varying flow velocity, the equation, of motion derived here exposes an error in a previous derivation. Stability, maps are presented for parametric instabilities, computed by Bolotin's method, for pipes with pined or clamped ends, as well as for cantilevered pipes. It is found that the extent of the instability regions increases with flow velocity for clamped-clamped and pinned-pinned pipes, while a more complex behaviour obtaines in the case of cantilevered pipes. In all cases, dissipation reduces the extent of, or entirely eliminates, parametric instability zones.