Possibilistic Interpretation of Mistuning in Bladed Disks by Fuzzy Algebra

Abstract

In the study of effect of mistuning on the dynamic response analysis of bladed disk systems, in literature, probabilistic methods are used. Conversely, in this paper, mistuning will be investigated by possibilistic analysis where mistuning parameters are modeled as fuzzy variables possessing possibility distributions. Fuzzy forced response characteristics of mistuned bladed disk systems are determined by mathematical basis of fuzzy sets. In order to do so, extension principle solution of fuzzy functions is used which overcomes the dependency issue problem observed on interval arithmetic solutions; hence, enhancing solution accuracy. Membership function distributions are digitized using alpha-cut methodology, slicing distributions to levels of confidence. Bounds of fuzzy variables in each and every level of confidence are determined using genetic optimization. Using this method, fuzzy forced response characteristics of a cyclically symmetric lumped parameter bladed disk model is determined. The possibilistic interpretation of mistuning is exemplified by determining the bounds of the possible maximum blade forced responses of the system for different orders of engine order excitation and by determining worst-possible case.