Interactions Between Self and Parametrically Excited Motions in Articulated Tubes

Abstract

The nonlinear dynamics of a two-segment articulated tubes system conveying a fluid is studied when the flow is harmonically perturbed. The mean value of the flow rate is near its critical value when the downward vertical position gets unstable and undergoes Hopf bifurcation into periodic solutions. The harmonic perturbations are assumed to be in parametric resonance with the linearized system. The method of Alternate Problems is used to obtain the small nonlinear subharmonic solutions of the system. It is shown that, in addition to the usual jump response, the system also exhibits stable and unstable isolated solution branches. For some parameter combinations the stable solutions can become unstable and can then bifurcate into aperiodic or amplitude-modulated motions.