Stability and chaotic vibrations of a fluid-conveying pipe with additional combined constraints

Abstract

The stability and possible chaotic vibrations of a fluid-conveying pipe with additional combined constraints are investigated. The pipe, restrained by motion constraints somewhere along the length of the pipe, is modeled by a beam clamped at the left end and supported by a special device (a rotational elastic constraint plus a Q-apparatus) at the right end. The motion constraints are modeled by both cubic and trilinear models. Based on the Differential Quadrature Method (DQM), the nonlinear dynamical equations of motion for the system are formulated, and then solved via a numerical iterative technique. Calculations of bifurcation diagrams, phase portraits, time responses and Poincare maps of the oscillations establish the existence of chaotic vibrations. The route to chaos is shown to be via period-doubling bifurcations. It is found that the effect of spring constant of the rotational elastic constraint on the dynamics is significant. Moreover, the critical fluid velocity at the Hopf bifurcation point for the cubic model is higher than that for the trilinear model.