Stability and bifurcation of a rigid rotor in cavitated squeeze-film dampers without centering springs

The continuation method is employed to investigate the non-linear response of a rigid rotor supported by squeeze-film dampers without centering springs. The Floquet transition matrix method, which was used to examine the stability of the periodic response, indicated that the rotor may lose stability via period-doubling and saddle-node bifurcations at certain parameter values. The continuation method, which allows for switching from one solution branch to another, enabled the solution branches of period-two, four, eight and sixteen to be mapped out. By simultaneously varying the unbalance and bearing parameters, the combination of these two parameters that avoids the occurrence of non-synchronous vibration or jump phenomena in this system was determined.