Triggering Mechanisms of Limit Cycle Oscillations in a Two Degree-of-Freedom Wing Flutter Model

Abstract

We show numerically that the triggering mechanisms of limit cycle oscillations (LCOs) due to aeroelastic instability are composed of a series of resonance captures. We consider a two degree-of-freedom (DOF) wing model with cubic nonlinear stiffnesses in the support, assuming quasi-steady aerodynamics and subsonic flow around the wing. Then, we establish the slow flow dynamics model, using the complexification / averaging technique and considering three frequency components; i.e., the two linear natural frequencies corresponding to heave and pitch and the superharmonic component which appears as three times the pitch frequency. It turns out that the LCO triggering mechanisms consist of mainly three stages: (i) transient resonance capture (TRC); (ii) escape; and (iii) permanent resonance capture (PRC). We examine the characteristics of each stage by way of time response, wavelet transform, phase plane, and instantaneous energy.