Maximum amplification of blade response due to mistuning: Localization and mode shapes aspects of the worst disks

This paper focuses on the determination and study of the maximum amplification of the steady state forced response of bladed disks due to mistuning. First, an optimization strategy is proposed in which 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 approach is exemplified on both a reduced order model of a blisk and a single-degree-of-freedom per blade disk model an extensive parametric study of which 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, the upper bound of Whitehead is recovered for all engine orders and 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 disk.