Localization Phenomena in Mistuned Assemblies with Cyclic Symmetry Part II: Forced Vibrations

The effects of disorder on the forced response of nearly periodic structures with cyclic symmetry are investigated. The force model adopted here is relevant to blade assemblies. Perturbation methods for the forced response are developed to gain a physical insight into the effects of mistuning. The study shows that the internal coupling between component systems is the key parameter governing the sensitivity to mistuning and that localized forced vibrations do occur in the disordered assembly for weak internal coupling. However, although both localized free and forced vibrations occur for finite or large values of the mistuning to coupling ratio, the deflection patterns for these two types of localized vibrations are different. Also, for the forced response, the degree of localization does not necessarily increase as this ratio increases—a fundamental difference from localized free modes. An important conclusion is that the common periodicity assumption for cyclic structures may lead to qualitative errors for the forced response of weakly coupled systems when small mistuning is present.