Enhancing the robustness of aeroelastic instability suppression using multi-degree-of-freedom nonlinear energy sinks

In this last of a three paper sequence, we use simultaneous multimodal broadband targeted energy transfers to multi-degree-of-freedom nonlinear energy sinks to improve the robustness of aeroelastic instability suppression of a rigid wing with structural nonlinearities. A numerical bifurcation analysis of limit cycle oscillations of the wing with the multi-degree-of-freedom nonlinear energy sinks attached shows that controlling the lower parameter value for limit point cycle bifurcation to occur above Hopf bifurcation is crucial to enhancing the robustness of limit cycle oscillation suppression. We demonstrate that multi-degree-of-freedom nonlinear energy sinks can greatly enhance the robustness of limit cycle oscillation suppression, compared with single-degree-of-freedom nonlinear energy sinks (which were studied in our previous papers), with a much smaller total mass. We also investigate the nonlinear modal interactions that occur between the aeroelastic modes and the multi-degree-of-freedom nonlinear energy sinks, in an effort to gain a physical understanding of the mechanisms governing instability suppression. We demonstrate that a properly designed multi-degree-of-freedom nonlinear energy sink provides robustness of aeroelastic instability suppression by efficiently, passively, and rapidly transferring a significant portion of unwanted vibration energy to the furthest mass of the nonlinear energy sink. Consideration of other types of multi-degree-of-freedom nonlinear energy sinks suggests that the robustness enhancement is achieved by the concentrated mass effect of the attached nonlinear energy sinks.