Nonlinear Dynamics of a Fluid-Conveying Cantilevered Pipe With a Small Mass Attached at the Free End

Abstract

Abstract In this paper, the planar dynamics of a fluid-conveying cantilevered pipe with a small mass attached at the free end (’end-mass’, for short) is examined theoretically and experimentally. An experimental study is undertaken with elastomer pipes conveying water, with metal or plastic end-masses. The main purpose is to extend the work of Copeland and Moon on a modified configuration: the motion is constrained to be planar instead of three-dimensional, and the pipe is modelled as a beam having a non-negligible flexural rigidity instead of a string hanging under gravity. As in previous studies, it is demonstrated that for the system with no end-mass, only one stable periodic solution exists, at least for the parameters considered. On the other hand, in the presence of a small end-mass, the dynamics is much richer and different types of periodic solutions are found to exist. Jump phenomena as well as chaotic oscillations are observed both in the experiments and numerically, revealing the importance of even a small mass on the dynamics. Qualitative and quantitative agreement between theory and experiments is rather good.