A novel limit distribution for the analysis of randomly mistuned bladed disks

A recently introduced perturbation technique is employed to derive a novel closed form model for the probability density function of the resonant and near-resonant, steady state amplitude of blade response in randomly mistuned disks. In its most general form, this model is shown to involve six parameters but, in the important practical case of a pure stiffness (or frequency) mistuning, only three parameters are usually sufficient to completely specify this distribution. A series of numerical examples are presented that demonstrate the reliability of this three-parameter model in accurately predicting the entire probability density function of the amplitude of response, and in particular the large amplitude tail of this distribution, which is the most critical effect of mistuning.