Nonlinear switching between flutter and forced response in bladed disks

Flutter and forced response are two effects that typically occur simultaneously in turbomachinery systems. The linear superposition of their separate contributions does not correctly estimate the vibration amplitude, since their interaction is nonlinear due to friction present at the contact interfaces of the blades with the disk. In previous works, it was shown that the presence of both effects in the system produces two different regions: near the resonance peak, the solution is synchronous with the forcing (locked), and, away from the resonance, flutter solutions are present. These results were obtained using a series of time integrations, which required a large number of cycles to converge. In this paper, the synchronous solutions with the forcing are obtained analytically and numerical continuation tools are used to track the other possible solutions of the system, along with their stability behavior. This approach is used to compute the bifurcation diagrams for different excitation cases, while avoiding the uncertainty and long integrations times associated with simulations in time. Nonlinear switching between flutter and forced response is present in all cases and, when forcing a very aerodynamically stable traveling wave in a rotor with an even number of blades, new frequency locked solutions are found, which, in a tuned rotor, show different blade vibration amplitudes. For odd blade counts, the structure of these new solutions is also present, with a disturbance traveling around the bladed disk.