The computation of the friction saturated vibratory response of an aerodynamically unstable bladed-disk in a realistic configuration is a formidable numerical task, even for the simplified case of assuming the aerodynamic forces to be linear. The nonlinear friction forces effectively couple different traveling waves modes and, in order to properly capture the dynamics of the system, large time simulations are typically required to reach a final, saturated state. Despite of all the above complications, the output of the system (in the friction micrvslip regime) is not that complex: it typically consists of a superposition of the aeroelas-tic unstable traveling waves, which oscillate at the elastic modal frequency and exhibit also a modulation in a much longer time scale. This large time modulation over the purely elastic oscillation is due to both, the small aerodynamic effects and the small nonlinear friction forces. The correct computation of these two small effects (small as compared with the elastic forces) is crucial to determine the final amplitude of the flutter vibration, which basically results from its balance. In this work we apply asymptotic techniques to obtain a new simplified model that gives only the slow time dynamics of the amplitudes of the traveling waves, filtering out the fast elastic oscillation. The resulting asymptotic model is very reduced and extremely cheap to simulate, and it has the advantage that it gives precise information about how the nonlinear friction at the fir-tree actually acts in the process of saturation of the vibration amplitude.
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