Localization Phenomena in Mistuned Assemblies with Cyclic Symmetry Part I: Free Vibrations

Abstract

An investigation of the effects of small structural irregularities on the dynamics of nearly periodic structures with cyclic symmetry is presented. The system studied may be regarded as a simple model of a continuously shrouded blade assembly accounting for one structural mode per blade. A key aspect of the approach is the use of perturbation methods that lead to a physical insight into the effects of mistuning. The study shows that the sensitivity to mistuning depends primarily upon the ratio of mistuning strength to coupling strength. For a small mistuning to coupling ratio, the mistuned system behaves like a perturbation of the corresponding tuned system, in which case mistuning has a relatively small effect on both the free and forced responses. On the other hand, for a large mistuning to coupling ratio (i.e., weak coupling), the mistuned system behaves like a perturbation of the corresponding decoupled mistuned system, in which case small mistuning dramatically changes the dynamics of the system. This paper, Part I, investigates the effects of small mistuning on the free response of the system. Specifically, it is shown that strong mode localization and eigenvalue loci veering phenomena occur in the weakly coupled system when mistuning is introduced. The effects of mistuning on the forced response are studied in the companion paper, Part II (Wei and Pierre, 1987).