A Mode-Accelerated XXr (MAX) method for complex structures with large blends

Abstract

Various reduced order models have been proposed for characterizing cyclic symmetric structures with complex geometry and varying material properties that are subject to complex boundary or loading conditions. Small variations can be represented as small mass or stiffness mistuning. Techniques developed to handle such variations rely on the fact that the modes of the system can be accurately approximated using a linear combination of modes of the healthy/nominal system. Such approximations are valid in regions of high modal density, but they break down when variations are large or geometric changes are present. To address this challenge, a novel method is presented to predict the vibration response of cyclic symmetric structures with large geometric changes due to damage in the form of missing material (blends). The central idea of the new approach is an extension of the XXr method for cracked structures. The XXr method was developed for modeling small mistuning and large cracks. That method is extended in this work to handle large blends. In addition, a specialized component mode synthesis is combined with the extended XXr method to maintain accuracy. Also, unique to the proposed novel method is a technique to accelerate the convergence of the order reduction, and thus obtain very low order models. These low order models provide excellent computational speed and effectiveness while maintaining accuracy. Therefore, the method can be applied to highly refined, realistic models of industrial size. To demonstrate the proposed mode-accelerated XXr method, the effects of large blends on the response of a bladed disk are investigated.