Pipes conveying pulsating fluid near a 0 : 1 resonance: Global bifurcations

We study the global dynamics of parametrically excited pipes conveying fluid near a 0 : 1 resonance. A major goal of the analysis is to understand how energy may be transferred from the high-frequency mode to the low-frequency mode in these systems. We study the bifurcations of supported pipes conveying fluid, focusing on the subharmonic resonance case. Finally, using recently developed global bifurcation methods, we detect the presence of orbits which are homoclinic to certain invariant sets for the resonant case. In the dissipative case, we are able to identify conditions under which a generalized Šilnikov orbit would exist. In certain parameter regions, we prove that such orbits exist which are homoclinic to fixed points on the slow manifold, leading to chaotic dynamics in the system. These orbits provide the mechanism by which energy transfer between modes may occur.