Analysis of a piecewise linear aeroelastic system with and without tuned vibration absorber

The dynamics of a two-degrees-of-freedom (pitch-plunge) aeroelastic system is investigated. The aerodynamic force is modeled as a piecewise linear function of the effective angle of attack. Conditions for admissible (existing) and virtual equilibria are determined. The stability and bifurcations of equilibria are analyzed. We find saddle-node, border collision and rapid bifurcations. The analysis shows that the pitch-plunge model with a simple piecewise linear approximation of the aerodynamic force can reproduce the transition from divergence to the complex aeroelastic phenomenon of stall flutter. A linear tuned vibration absorber is applied to increase stall flutter wind speed and eliminate limit cycle oscillations. The effect of the absorber parameters on the stability of equilibria is investigated using the Lienard-Chipart criterion. We find that with the vibration absorber the onset of the rapid bifurcation can be shifted to higher wind speed or the oscillations can be eliminated altogether.