Aeroelastic Stability at High Advance Ratios: A Novel Floquet Theory Approach with Multi-Degree-of-Freedom Modal Waveform Analysis

High speed compound rotorcraft may operate with slowed rotors, resulting in high advance ratios and aeroelastic instabilities. The classic Floquet approach to understanding this periodic system was expanded using a hybrid symbolic and computational method, incorporating coupled flap-lag-torsion degrees of freedom, reverse flow, unsteady aerodynamics, and a realistic trim routine bounded by thrust reversal and blade stall. A novel eigenvalue tracking algorithm and modal waveform analysis of the eigenvector motion was developed to generate and identify root loci, providing fundamental insights into parametric resonance and other instabilities. Advance ratios above 3 were explored, with parametric evaluations of both physical dynamic stability and numerical stability. The model's predictions were validated using historical analyses and experimental results, and recommendations regarding stable configurations are provided.