A Novel Perturbation-Based Approach for the Accurate Prediction of the Forced Response of Mistuned Bladed Disks

Abstract

This paper focuses on the formulation and validation of a novel perturbation method for the prediction of the forced response of mistuned bladed disks. At the contrary of previous approaches, the proposed one involves the sum of the inverses of the tuned and mistuned impedance matrices through the use of the Sherman-Morrison-Woodbury formula. Then, considering these inverses as diagonal dominant matrices leads to an efficient series representation of the forced response of mistuned bladed disks. A detailed validation effort of this new procedure was next achieved. In particular, it was demonstrated that this approach leads to a convergent series representation over the entire range of blade-disk coupling levels for small mistuning. The dominant parameter affecting the magnitude of the largest mistuning for which convergence occurs is shown to be the system damping with a weaker effect of the blade-disk coupling. Examples of application to a single-degree-of-freedom per blade model and the reduced order model of a blisk demonstrate the potential of this novel approach. Finally, the applicability of this technique for the optimization of intentional mistuning pattern is shown.