A note on the stability and chaotic motions of a restrained pipe conveying fluid

In this note, the stability and chaotic motions of a standing pipe conveying fluid is studied and further compared with that of a hanging system developed by Jin [1]. The standing pipe involves elastic support and motion-limiting constraints, producing a nonlinear force on the pipe as the motion becomes large. Based on numerical calculations, bifurcation diagram, time trace and phase portrait of the oscillations are obtained. It is shown that the dynamics of the standing pipe is much richer than that of the hanging system. The effect of elastic spring stiffness on the global dynamics of the standing pipe conveying fluid is also discussed.