Periodic Ground Resonance Analysis with Non-Linear Elements using Harmonic Decomposition and Describing Functions

Ground resonance, a self-excited instability typical of helicopters, that can lead to catastrophic failure. Its analysis becomes particularly complex in non-symmetric rotor configurations, such as those with an inoperative damper, which give rise to Linear Time-Periodic (LTP) systems. The stability investigation of the equations of motion can be handled through the Floquet method of characteristic exponents, or with the more recent linear time-invariant (LTI) harmonic decomposition (HD) method. The two methods are presented and their relationship is explored through Hill's infinite matrix and its modal solutions. Numerical results are given for rotors with different blade counts and two damper arrangements—blade-to-hub (BH) and interblade (IB)—under single and multiple damper failure conditions. A minimum-harmonics rule is derived that links the required number of harmonic terms directly to the multi-blade coordinate (MBC) structure of the rotor. Finally, the LTI state-space system produced by the HD is coupled with a describing-function framework to extend the stability analysis to rotors equipped with nonlinear dampers, enabling efficient limit-cycle prediction without recourse to time integration.