A Rubin-Based Reduced Order Model for Mistuned Bladed Disks: A Physically Interpretable and Experimentally Compatible Approach

The dynamic design of bladed disks is typically carried out under the assumption of ideal cyclic symmetry. In practice, however, manufacturing tolerances and assembly operations unavoidably introduce deviations in both stiffness and mass of each sector from their nominal values. This results in a mistuned assembly, which can lead to significantly higher blade vibration levels compared to the nominally tuned disk. Although full finite element (FE) models can be used to predict the response of mistuned bladed disks, the highly refined meshes employed by the designers in commercial FE software often make such analyses computationally expensive, sometimes even at the single-sector level under cyclic symmetry conditions. For this reason, the use of reduced-order models (ROMs) remains an effective strategy to enable feasible dynamic analyses for large-scale FE models. Traditionally, ROMs for mistuned bladed disks are based on fixed-interface methods. However, when the model must incorporate experimentally measured free-vibration modes of the blades, as well as the actual contact conditions between blades and disk slots, fixed-interface methods become limited. This is because they rely on perturbing the eigenvalues of fixed-interface normal modes, which require strong assumptions about the interface constraints—assumptions that may differ significantly from the real contact conditions. In this work, a novel ROM method for mistuned bladed disks is proposed, based on the Rubin method, which belongs to the class of free-interface methods. This formulation allows the use of free–free blade modes, which can be reliably measured experimentally and are independent of blade–disk boundary conditions. The resulting model provides a simpler, more robust, and physically meaningful framework for the prediction of mistuned bladed-disk dynamics. Comparisons with full FE models demonstrate that the proposed method is straightforward to implement, physically interpretable, and capable of accurately capturing both small and large mistuning.