Local/global effects and maximum amplification of blade forced response in mistuned turbomachinery disks

The focus of the present investigation is on the prediction of the forced vibration response of mistuned bladed disks, i.e. those exhibiting small deviations from a perfect rotational symmetry. Two main aspects of this problem are specifically addressed: the assessment and modeling of the local (spanning only a few blades) and global (encompassing the entire disk) effects of mistuning and the determination of the highest amplification of blade response due to mistuning in a worst-case scenario.; The concept of wave localization is revisited, and a new measure of this effect is introduced that is based on partially mistuned disks, i.e. those exhibiting mistuned blades in a sector only. Using this new metric, it is demonstrated that high responding blades are typically characterized by a high level of localization but that the reverse is not true. Thus, localization is not only disk-dependent but also varies from blade-to-blade on the same disk. Based on these observations and on the modeling of local and global effects of mistuning, novel expedient computational techniques are devised to accurately predict the forced response of the bladed system through the entire range of blade-to-blade coupling.; Next, an optimization strategy is formulated for the determination of the highest amplification of blade response due to mistuning. In this approach, partially mistuned bladed disks are considered as physical approximations of the worst-case disk and the mistuned properties are sought to maximize the response of a specific blade. This strategy is exemplified on both a reduced-order model of a blisk and a single-degree-of-freedom per blade disk model of which an extensive parametric study is conducted with respect to blade-to-blade coupling, damping, and engine order. A mode shape-based formulation of the amplification factor is then developed to clarify the findings of the parametric study in the strong coupling/small damping limit. In this process, an existing upper bound to this amplification factor is recovered for all engine orders, and the number of blades and the conditions under which this limit is exactly achieved or closely approached are clarified. This process also uncovers a simple yet reliable approximation of the resonant mode shapes and natural frequencies of the worst-case disk.