A simple model that describes the non-linear dynamics of bladed-disk due to the dry friction exerted in attachment and the unsteady aerodynamic forced 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 multi-mode 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 using simplified models.

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