Spatially localized vibrations in a rotor subjected to flutter

The current push toward lightweight structures in aerospace and aeronautical engineering is leading to slender design airfoils, which are more likely to undergo large deformation, hence experiencing geometrical nonlinearities. The problem of vibration localization in a rotor constituted by N coupled airfoils with plunge and pitch degrees of freedom subjected to flutter instability is considered. For a single airfoil, it is shown that depending on the system parameters, multiple static and dynamic equilibria coexist which may be a fixed point, a limit cycle, or irregular motion. By elastically coupling N airfoils, a simplified rotor model is obtained. The nonlinear dynamical response of the rotor is studied via time integration with particular attention to the emergence of localized vibrating solutions, which have been classified introducing a localization coefficient. Finally, the concept of basin stability is exploited to ascertain the likelihood of the system to converge to a certain localized state as a function of the airstream velocity. We found that homogeneous and slightly localized states are more likely to appear with respect to strongly localized states.