Optimal Design of Intentional Mistuning for A Bladed Disk with Interval Uncertainty

This paper presents a methodology for the optimal design of intentional mistuning for a mistuned bladed disk with interval uncertainty. For a bladed disk where blades are weakly coupled, presence of random mistuning can easily induce vibration localization. This phenomenon will lead to great amplification in response amplitude of certain blades. To achieve desired reliability of a bladed disk, amplified response must be reduced to certain level, which requires probabilistic or reliability analysis. In this study, it is considered that blades have random distribution and coupling between blades has interval uncertainty. To treat the interval uncertainty appropriately, the worst-case combination of interval couplings is searched first, then probability of failure is evaluated under the worst-case condition. To increase reliability of a bladed disk, intentional mistuning is used in this study. While applying the intentional mistuning, it is also wanted to minimize the degree of intentional mistuning to minimize the cost of implementation. To find optimal combination of intentional mistuning parameters to achieve dual goals, gradient-based design optimization approach is utilized, which is expected to guarantee efficient convergence. To carry out gradient-based design optimization, sensitivities of objective function and probabilistic constraints with respect to intentional mistuning parameters are derived. During the sensitivity analysis, distribution of forced response amplitude is identified through Gaussian fit and eigenvalue perturbation theory is referred to. Monte Carlo simulation is utilized to accurately calculate probability of failure and its sensitivity. The proposed method is demonstrated with numerical examples of two distinct bladed disks.