A Unified Assessment of Fast Floquet, Generalized Floquet, and Periodic Eigenvector Methods for Rotorcraft Stability Predictions

This paper presents a unified assessment of fast Floquet, generalized Floquet, and generalized fast Floquet theories, as alternatives to Floquet theory, in predicting rotorcraft stability. For a rotor with Q identical blades, fast Floquet reduces Q-fold the computing time as well as frequency indeterminacy of Floquet theory; so is the case between generalized Floquet and generalized fast Floquet theories. (Both Floquet and fast Floquet theories require complete state-space modeling, whereas the other two permit incomplete state-space modeling.) This assessment includes how the mode identification from Fourier series analysis of periodic eigenvectors lends itself well to large systems, say with about 400 states. Other key features include extension of earlier proposed Floquet mode identification to fast Floquet theory and correlation of identified modes with test data, which include ground resonance and mode-to-mode similarity. In combination with Fourier analysis of periodic eigenvectors, fast Floquet theory provides a practical means of exactly identifying the modes and predicting the stability margins of large systems.