Vibration Absorbers for Cyclic Rotating Flexible Structures: Linear and Nonlinear Tuning

The nonlinear performance of centrifugally-driven, order-tuned absorbers is investigated for vibration reduction of a cyclic rotating flexible structure under traveling wave (TW) engine order excitation. A key finding from previous work by the authors using a linearized model is the existence of a no-resonance zone, that is, an entire range of absorber designs that avoid system resonance for any rotation speed. Linearization is generally valid for the rotating structure but absorber motions can become large for typical loading conditions. This work generalizes the linear results to account for large-amplitude, nonlinear absorber motions. Existence and stability of the steady-state TW response to TW excitation are investigated in terms of the absorber path design, which fixes its linear and nonlinear tuning characteristics. A TW response is unique for the linearized system and is shown to exist for the weakly nonlinear model. The nonlinear model exhibits the usual characteristics of a weakly nonlinear system, including bistability and the attendant hysteresis near resonance. More significantly, no additional instabilities associated with the symmetry could be identified. Hence the desired TW response is robust to nonlinear absorber effects and can be described by an equivalent model, which is obtained by reduction using the symmetry. It is shown that good performance can be obtained by linear absorber tuning in the no-resonance zone and the absorber paths should have a slightly softening nonlinear characteristic.