Stability and Bifurcation Analysis of the Transverse Vibrations of a Cantilever Pipe Conveying Pulsating Two Phase Flow

This work presents analytical and numerical analysis of the stability and bifurcation of a cantilevered pipe conveying pulsating two phase flow. Multiple scale perturbation technique is used to obtain the stationary trivial and nontrivial solutions of its response amplitudes. Clearly, the system exhibits both stable and unstable solutions depending on the detuning of the frequencies. The fixed point of the non trivial solutions of the pipe’s dynamics is a saddle node bifurcation. On the other hand, trajectories of the trivial solutions present subcritical pitchfork and supercritical pitchfork bifurcations at the critical points. Numerical simulations are observed to be in agreement with analytical results. Also, a study on the effect of void fraction on the bifurcation points shows that at post-critical mixture velocity, a defining void fraction exists when there is a transition between the subcritical pitchfork bifurcation point and supercritical pitchfork bifurcation.