Abstract
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.
Highlights
There are several examples in engineering for structures constituted by mechanical elements arranged in a cyclic and symmetric fashion, which range from aeroengine fans [1], turbine and compressor rotors [2], wind turbine rotors [3], propellers [4], blisks [5] and space structures [6,7,8]
The nonlinear dynamical behavior of a rotor constituted by N = 3 slender airfoils with 2-DOF each and subjected to flutter instability has been studied
By restricting the state space to a certain hypervolume of initial conditions, the concept of basin stability has been exploited to determine the likelihood of the system to converge to localized states
Summary
There are several examples in engineering for structures constituted by mechanical elements arranged in a cyclic and symmetric fashion, which range from aeroengine fans [1], turbine and compressor rotors [2], wind turbine rotors [3], propellers [4], blisks [5] and space structures [6,7,8]. Small deviations in the inertia or elastic properties of the rotor blades (unavoidable due to the manufacturing tolerances and wear) substantially change the underlying mode shapes of the system leading to spatial localization of vibration, up to remarkable amplification factor, e.g., about 6 in a rotor with 121 blades [11] ( extreme cases are unlikely to happen) Such an event may be life-threatening for the blade [13,14,15], design strategies opt for considerable damping when large vibration amplitudes are reached, e.g., by introducing frictional dampers [16,17,18,19,20]. The claim for high power output and low energy consumption constantly pushes the design of newgeneration turbomachinery toward larger rotors with higher blade aspect-ratio (see Fig. 1) Slender blades, alike those in the new-generation turbofan [41] or in wind turbines, undergoing large deformations are a perfect candidate to show localization in weakly coupled structures. It is shown that the system more likely converges on homogeneous or slightly localized solutions, while strongly localized states are restricted to a quite narrow range of airstream velocity
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