Flutter is a major constraint on modern turbomachines; as the designs move toward more slender, thinner, and loaded blades, they become more prone to experience high cycle fatigue problems. Dry friction, present at the root attachment for cantilever configurations, is one of the main sources of energy dissipation. It saturates the flutter vibration amplitude growth, producing a limit cycle oscillation whose amplitude depends on the balance between the energy injected and dissipated by the system. Both phenomena, flutter and friction, typically produce a small correction of the purely elastic response of the structure. A large number of elastic cycles is required to notice their effect, which appears as a slow modulation of the oscillation amplitude. Furthermore, even longer time scales appear when multiple traveling waves are aerodynamically unstable and exhibit similar growth rates. All these slow scales make the system time integration very stiff and CPU expensive, bringing some doubts about whether the final solutions are properly converged. In order to avoid these uncertainties, a numerical continuation procedure is applied to analyze the solutions that set in, their traveling wave content, their bifurcations and their stability. The system is modeled using an asymptotic reduced order model and the continuation results are validated against direct time integrations. New final states with multiple traveling wave content are found and analyzed. These solutions have not been obtained before for the case of microslip friction at the blade attachment; only solutions consisting of a single traveling wave have been reported in previous works.

The wind tunnel facility at the Centro de Tecnologías Aeronáuticas was used to perform a set of experiments to study the effect of intentional mistuning on the forced response behavior of an aerodynamically unstable low-pressure turbine rotor. The intentional mistuning patterns were implemented by adding a small extra mass to some of the blades. The forced response of the rotor was therefore expected to show two resonance peaks with similar amplitudes, corresponding, respectively, to the vibration frequencies of the blades with and without added mass. However, on the post-processing of the measurements, some anomalous behavior was observed. Near resonance, the system response was synchronous with the forcing, and the frequency sweeps exhibited two resonance peaks, but it was found that the two peaks were clearly different, with the peak at lower frequency showing a much higher vibration amplitude than the high-frequency peak, and with some blades responding at both frequencies with a similar amplitude. In order to give a correct interpretation of the experimental results, a reduced-order model is derived that takes into account only the traveling wave modes coupled by the mistuning. This model, although extremely simple, is capable of reproducing the unexpected behavior of the experiments, and gives a clean explanation of the system response. It is shown that the relative size of the mistuning with respect to the frequency difference of the involved traveling-wave modes is the key parameter for the appearance of this phenomenon.

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