Suppressing Aeroelastic Instability Using Broadband Passive Targeted Energy Transfers, Part 1:Theory

We study passive and nonlinear targeted energy transfers induced by resonant interactions between a singledegree-of-freedom nonlinear energy sink (NES) and a 2-DOF in-flow rigid wing model.We show that it is feasible to partially or even completely suppress aeroelastic instability by passively transferring vibration energy from thewing to the NES in a one-way irreversible fashion. Moreover, this instability suppression is performed by partially or completely eliminating its triggering mechanism. Numerical parametric studies identify three main mechanisms for suppressing aeroelastic instability: recurring burstout and suppression, intermediate suppression, and complete elimination.We investigate thesemechanisms both numerically by theHilbert–Huang transformand analytically by a complexification-averaging technique. Each suppressionmechanism involves strong 1:1 resonance capture during which the NES absorbs and dissipates a significant portion of energy fed from the flow to the wing. Failure of suppression is associated with restoring the underlying triggering mechanism of instability, which is a series of superharmonic resonance captures followed by escapes from resonance. Finally, using a numerical continuation technique, we perform a bifurcation analysis to examine sensitive dependence on initial conditions and thus robustness of instability suppression.