The focus of the present investigation is on the assessment and modeling of the local (spanning only a few blades) and global (encompassing the entire disk) effects of mistuning on the forced response of bladed disks. To this end, the concept of localization is first revisited and a new measure of this effect is introduced in terms of the number of blades the mistuning of which actually affects the forced response of a central blade. Using this new metric, it is demonstrated that high responding blades typically exhibit a high level of localization and that the reverse is not necessarily true. Thus, localization is not only disk dependent but also varies from blade-to-blade on the same disk. This observation is then used to validate a partial mistuning approach to the determination of the maximum amplitude of response over the entire population of disks. The results of this study indicate that the largest amplification due to the mistuning occurs at very strong blade-to-blade coupling levels, at the contrary of a general perception, but is associated with large mistuning levels. Finally, the above phenomenological observations are used to devise a modeling technique of both local and global components of mistuning. An example of application is presented that demonstrates the high accuracy of this approach through the entire blade-to-blade coupling domain.

The focus of the present investigation is on the assessment and modeling of the local (spanning only a few blades) and global (encompassing the entire disk) effects of mistuning on the forced response of bladed disks. To this end, the concept of localization is first revisited and a new measure of this effect is introduced in terms of the number of blades the mistuning of which actually affects the forced response of a central blade. Using this new metric, it is demonstrated that high responding blades typically exhibit a high level of localization and that the reverse is not true. Thus, localization is not only disk dependent but also varies from blade-to-blade on the same disk. This observation is then used to validate a partial mistuning approach to the determination of the maximum amplitude of response over the entire population of disks. The results of this study indicate that the largest amplification due to mistuning occurs at very strong blade-to-blade coupling levels, at the contrary of a general perception, but is associated with extremely large mistuning levels. Finally, the above phenomenological observations are used to devise a modeling technique of both local and global components of mistuning. An example of application is presented that demonstrates the high accuracy of this approach through the entire blade-to-blade coupling domain.

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.

The focus of the present investigation is on the use of intentional mistuning of bladed disks to reduce their sensitivity to unintentional random mistuning. The class of intentionally mistuned disks considered here is limited, for cost reasons, to arrangements of two types of blades (A and B, say). A two-step procedure is then described to optimize the arrangement of these blades around the disk to reduce the effects of unintentional mistuning. First, a pure optimization effort is undertaken to obtain the pattern(s) of the A and B blades that yields small/the smallest value of the largest amplitude of response to a given excitation in the absence of unintentional mistuning. Then, in the second step, a pattern screening technique based on a recently introduced measure of localization is used to determine which of the patterns does have a large/small sensitivity to random unintentional mistuning. In this manner, expensive Monte Carlo simulations can be eliminated. Examples of application involving both simple bladed disk models and a 17-blade industrial rotor clearly demonstrate the significant benefits of using this class of intentionally mistuned disks.

The focus of the present two-part investigation is on the estimation of the dynamic properties, i.e., masses, stiffnesses, natural frequencies, mode shapes and their statistical distributions, of turbomachine blades to be used in the accurate prediction of the forced response of mistuned bladed disks. As input to this process, it is assumed that the lowest natural frequencies of the blades alone have been experimentally measured, for example, in a broach block test. Since the number of measurements is always less than the number of unknowns, this problem is indeterminate in nature. In this first part of the investigation, two distinct approaches will be investigated to resolve the shortfall of data. The first one relies on the imposition of as many constraints as needed to ensure a unique solution to this identification problem. Specifically, the mode shapes and modal masses of the blades are set to their design/tuned counterparts while the modal stiffnesses are varied from blade to blade to match the measured natural frequencies. The second approach, based on the maximum likelihood principle, yields estimates of all the structural parameters of the blades through the minimization of a specified “cost function.” The accuracy of these two techniques in predicting the forced response of mistuned bladed disks will be assessed on simple dynamic models of the blades.