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

We study the local bifurcation behavior 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 pipe systems, focusing on the subharmonic resonance case. We calculate the stability of the trivial solution, the bifurcating single-mode branches and their stability, and the existence of multi-mode or periodic solutions. Regions where energy transfer may occur from high- to low-frequency modes are identified. The numerical bifurcation analysis software AUTO97 is used to support the analytical results.