Dynamics of cantilevered pipes conveying fluid. Part 2: Dynamics of the system with intermediate spring support

This paper, the second in a three-part series, deals with the three-dimensional (3-D) nonlinear dynamics of a vertical cantilevered pipe conveying fluid, additionally constrained by arrays of four or two springs or a single spring at a point along its length. Theoretical calculations are presented for the same pipe but different spring configurations, points of attachment and stiffnesses, the main generic difference being this: in some cases, the system loses stability by planar flutter, and thereafter performs two-dimensional (2-D) or 3-D periodic, quasiperiodic and chaotic oscillations; in other cases, the system loses stability by divergence, followed at higher flows by oscillations in the plane of divergence or perpendicular to it, again periodic, quasiperiodic or chaotic. Experiments were conducted for some of the systems studied theoretically, and agreement is found to be generally good, although some open questions remain.