A great deal of research has been conducted on the effects of small random variations in structural properties, known as mistuning, in single stage bladed disks. Due to the inherent randomness of mistuning and the large dimensionality of the models of industrial bladed disks, a reduced order modeling approach is required to understand the effects of mistuning on a particular bladed disk design. Component mode mistuning (CMM) is an efficient compact reduced order modeling method that was developed to handle this challenge in single stage bladed disks. In general, there are multiple stages in bladed disk assemblies, and it has been demonstrated that for certain frequency ranges accurate modeling of the entire bladed disk assembly is required because multistage modes exist. In this work, a statistical characterization of structural mistuning in multistage bladed disks is carried out. The results were obtained using CMM combined with a multistage modeling approach previously developed. In addition to the statistical characterization, a new efficient classification method is detailed for characterizing the properties of a mode. Also, the effects of structural mistuning on the characterization of the mode is explored.

The high performance bladed disks used in today’s turbomachines must meet strict standards in terms of aeroelastic stability and resonant response level. One structural characteristic that can significantly impact on both these areas is that of bladed disk mistuning. To predict the effects of mistuning, computational efficient methods are much needed to make free-vibration and forced-response analyses of full assembly finite element (FE) models feasible in both research and industrial environments. Due to the size and complexity of typical industrial bladed disk models, one must resort to robust and systematic reduction techniques to produce reduced-order models of sufficient accuracy. The objective of this paper is to compare two prevalent reduction methods on representative test rotors, including a modern design industrial shrouded bladed disk, in terms of accuracy (for frequencies and mode shapes), reduction order, computational efficiency, sensitivity to intersector elastic coupling, and ability to capture the phenomenon of mode localization. The first reduction technique employs a modal reduction approach with a modal basis consisting of mode shapes of the tuned bladed disk which can be obtained from a classical cyclic symmetric modal analysis. The second reduction technique uses Craig and Bampton substructure modes. The results show a perfect agreement between the two reduced-order models and the nonreduced finite element model. It is found that the phenomena of mode localization is equally well predicted by the two reduction models. In terms of computational cost, reductions from one to two orders of magnitude are obtained for the industrial bladed disk, with the modal reduction method being the most computationally efficient approach.

Reduced-order models have been reported in the literature that can be used to predict the harmonic response of mistuned bladed disks. It has been shown that in many cases they exhibit structural fidelity comparable to a finite element analysis of the full bladed disk system while offering a significant improvement in computational efficiency. In these models the blades and disk are treated as distinct substructures. This paper presents a new, simpler approach for developing reduced-order models in which the modes of the mistuned system are represented in terms of a subset of nominal system modes. It has the following attributes: the input requirements are relatively easy to generate; it accurately predicts mistuning effects in regions where frequency veering occurs; as the number of degrees-of-freedom increases it converges to the exact solution; it accurately predicts stresses as well as displacements; and it accurately models the deformation and stresses at the blades’ bases.