Modal Analysis and Forced Response of Coupled Mistuned Cyclic Systems: A Singular Perturbation Approach

The effect of small deterministic parameter perturbations on the forced response of nearly periodic structures with cyclic symmetry has been investigated. The general theory developed herein is applicable to any n^th order strongly coupled cyclic system with two arbitrary and independent variations in system parameters that destroy the cyclic symmetry. The specific system studied may be regarded as a simplified model of a strongly coupled bladed-disk assembly. Singular perturbation methods along with modal expansion analysis are applied to gain a physical insight into the effects of perturbations on the eigenvalues, the eigenvectors as well as the forced response amplitudes. The study shows that, under appropriate conditions, the splitting and veering of eigenvalues due to mistunings or small parameter variations increases the amplitude of vibration of some blades quite significantly than would be predicted on the basis of an analysis of the perfectly tuned system. Further, the modal bifurcations lead to uneven vibration amplitudes irrespective of the stiffness of the coupling springs. The variation in blade amplitudes are also found to be strongly dependent on the type of engine order excitation for the same set of mistuning parameter.