Flutter of Mistuned Turbomachinery Rotors

An investigation of the fundamental aspects of flutter in mistuned turbomachinery rotors is presented. Perturbation methods are used to obtain asymptotic solutions to arbitrary order in the mistuning parameter. These solutions require only the knowledge of the eigensolution of the tuned system, and thus provide efficient formulas for calculating the effect of mistuning without solving a new eigenvalue problem. Numerical results presented for design parameters representative of fan rotors indicate that a critical reduced frequency exists, below which mistuning alone cannot stabilize the rotor. The sensitivity of the stability boundaries to mistuning was found to depend fundamentally on relations between the left and right eigenvectors. For systems where the left and right eigenvectors form complex conjugate pairs, mistuning cannot destabilize the system unless the reduced frequency of the least stable mode is decreased by the perturbation. In general, only cascades and rotors with a single degree-of-freedom per blade belong to this class.