Solving for mistuned forced response by symmetry

The introduction of mistuning in jet-engine bladed disks can lead to large changes in stability and forced response. Even small random mistuning (with in the hounds of manufacturing tolerance) can lead to unacceptable response and high-cycle fatigue, Meanwhile, intentional mistuning may improve stabi lity and forced response under manufacturing uncertainty. This paper presen ts a general framework for predicting forced response as a function of mist uning. Because the forced response problem is an almost-singular linear pro blem, its solution is highly nonlinear in the mistuning parameters. Our met hods exploit symmetry arguments and eigenstructure perturbation to provide a method valid for any model. II is shown that, by perturbing eigenvectors in the numerator and the inverse of eigenvalues in the denominator (exploit ing symmetry in both computations), we can accurately approximate the force d response as a function of mistuning. Results are demonstrated for a simpl e lightly damped model, and the consequent sharp nonlinear behavior is capt ured almost perfectly. We also show that intentional mistuning may guarante e improved stability and forced response under fixed manufacturing toleranc es. Thus, intentional mistuning should be considered as a practical means o f increasing safety and enhancing engine performance.