Dynamics of a pipe conveying pulsating flow near criticality

In this paper, we study the dynamics of a simply supported pipe conveying pulsating flow near the flow velocity where the system first becomes unstable. We study a Galerkin discretization of this system which involves the first two modes of the pipe, near the flow velocity where the two degree of freedom Hamiltonian system possesses a nonsemisimple double zero eigenvalue and a pair of imaginary axis eigenvalues. The damping, as well as the parametric forcing due to the pulsating flow, are considered as perturbations to a conservative system. Using local bifurcation analysis and recently developed global bifurcation methods, we study the transfer of energy from the forced high frequency mode to the unforced low frequency mode. This transfer of energy causes unwanted vibrations in the mode associated with the double zero eigenvalue, due to the 0 : 1 resonance that this mode has with the high frequency mode.