Maximum Resonant Response of Mistuned Bladed Disks

The turbomachinery bladed disks used in today’s advanced turbine engines must meet strict standards with regard to aeroelastic stability and forced resonant response. One structural characteristic of bladed disks that can significantly impact both of these areas is that of bladed disk mistuning. Mistuning occurs when some circumferential asymmetry exists in the bladed disk. This asymmetry can be due to such things as mass or stiffness eccentricity or slight variations in the individual blade properties and occurs in all bladed disks to a greater or lesser extent. One important structural phenomenon resulting from mistuning is the splitting of the bladed disk’s diametral modes of vibration into “twin” or “dual” modes. The presence of dual mode characteristics in a bladed disk can significantly affect either or both of its aeroelastic stability and resonant response characteristics. The present paper, expanding upon the earlier works of Tobias and Arnold [1] and of Ewins [2] addresses the prediction of the maximum resonant response of a mistuned bladed disk having closely spaced dual modes as a function of mode mistuning and modal damping. A closed form expression is derived for the maximum forced resonant response. A discussion of mistune and damping characteristics of typical turbomachinery bladed disks is also presented.