Three-dimensional dynamics of a fluid-conveying cantilevered pipe fitted with an additional spring-support and an end-mass

The three-dimensional (3-D) dynamics of a fluid-conveying cantilevered pipe fitted with an end-mass and additional intra-span spring-support is investigated in this paper, both theoretically and experimentally. The main objective is to examine how the dynamics of a cantilevered pipe with additional spring-support is modified by the presence of a small mass attached at the free end. In the theoretical study, the nonlinear three-dimensional equations of motion are discretized via Galerkinʹs method, and the resulting equations are solved by a finite difference method. For the cases studied, the system was found to lose stability by planar flutter; as the flow velocity is increased beyond that point, a sequence of higher order bifurcations ensue, involving 2-D and 3-D periodic and quasiperiodic motions, as well as chaotic ones. In the experiments, performed with elastomer pipes and water flow, similarly 2-D and 3-D periodic, quasiperiodic and chaotic oscillations were observed. Theory and experiments have been shown to be in good qualitative and quantitative agreement. The experimental behaviour is illustrated by video clips (electronic annexes). Moreover, the effects of (i) small stiffness imperfections and (ii) excitation by a point-force are explored theoretically in a preliminary way.