Exploiting internal resonances in nonlinear structures with cyclic symmetry as a mean of passive vibration control

The purpose of this paper is to study how internal resonances can be used to mitigate the vibration of cyclically symmetric systems exhibiting geometrical nonlinear effects. The method of multiple scales is employed to derive specific conditions that allow such energy transfers. This novelty is confirmed through numerical investigations, and an application to decrease the vibration of the system is proposed. A simplified yet realistic blade model with geometrical nonlinearities is considered. It includes pre-twist, pre-bending and warping, and is duplicated to create a full bladed rotor with cyclically symmetric properties. As the model of the whole structure may become enlarged, it is further reduced via the normal form approach. The harmonic balance method is then employed to obtain periodic solutions, localize bifurcation points and then follow bifurcated branches. These numerical solutions are used in complement with the aforementioned theoretical conditions to investigate the energy transfer properties of the mechanical system. Through these simulations, an effective range of amplitude excitation is defined to obtain internal resonances leading to an overall vibration mitigation of the system.