Nonlinear Dynamics of Bladed Disks with Multiple Unstable Modes

A simple model that describes the nonlinear dynamics of bladed disks due to dry friction exerted in the attachment of the rotor blades with the disk, and the unsteady aerodynamic forces induced by the vibration of aerodynamically unstable airfoils, is presented and analyzed. The analysis is focused on a simplified case whose dynamics is representative of a high aspect ratio low-pressure turbine rotor blade. A parametric study is conducted to understand the dynamics of the the problem for times much longer than the fundamental period of the rotor blades, when the effect of the initial conditions is not relevant and a periodic steady state has been reached. It is concluded that the conjecture that the dynamics of multimode unstable bladed disk, in the absence of external periodic forcing, finally reaches a state in which only a single traveling wave exists is true and that this behavior may be reproduced also using simplified models.