Suppression of limit cycle oscillations with a nonlineart energy sink: theoretical basis

Limit cycle oscillations (LCOs) commonly require restrictions on the operation of high-
performance aircraft and have the potential to cause structural damage or failure. This paper summarizes recent theoretical findings on the application of passive and targeted nonlinear energy transfer (\nonlinear energy pumping") for the reduction or elimination of LCOs in self-excited systems. This NES has been used successfully to suppress LCOs of an elastically mounted, rigid airfoil in flow. The theoretical results are in agreement with experimental studies of a practical airfoil with an attached NES. These experimental results, presented in full in a separate paper, verify the capacity of the NES to reduce or even eliminate these undesired oscillations and to extend the operating speed range of the wing.