Numerical investigation of the influence of gravity on flutter of cantilevered pipes conveying fluid

We have carried out a numerical investigation of the three dimensional nonlinear dynamics of a cantilevered pipe conveying fluid in the presence of gravity. The pipe may be misaligned at the clamped end with respect to gravity, and the effects of this misalignment are the main objects of the present investigation. The problem has been formulated using the Cosserat rod model. First, we have computed the equilibrium solutions and used them to experimentally validate both the Cosserat model and the constitutive law. Then, we have analyzed the occurrence of flutter, via Hopf bifurcation, for critical values of the relevant parameters of the problem, such as fluid to total mass ratio, dimensionless flow rate, dimensionless gravity and misalignment angle. The influence of the equilibrium solution on flutter has been explored, and the results of the linear stability analysis show that the stabilizing or destabilizing effect of fluid flow, either in or out of the plane of the pipe, depend crucially on the misalignment. We have also computed the non-linear periodic behavior after flutter instability by two different methods: the first one is by solving the full nonlinear equations by direct integration in time and space, while the second one is by assuming the time dependence given by an appropriate ansatz. Circular periodic orbits have then been studied and found that its loss of stability via Hopf bifurcation gives rise to stable planar periodic orbits. Finally, we have also computed the multiply periodic and chaotic behaviors which take place for sufficiently large values of the flow rate.