6. An Assessment on the Efficiency of Different Reduction Techniques Based on Substructuring for Bladed Disk Systems with Shrouds

Vibration analysis of shrouded bladed disk systems often becomes expensive due to friction nonlinearities and randomness stemming from mistuning phenomena. This implies a great demand for a highly efficient model order reduction technique to not only reduce the computational effort but, more importantly, provide reliable displacement predictions on certain degrees of freedom (shrouds). The latter becomes more critical in bladed disks with shroud contacts, since the promising results from contact models are limited by the accuracy of displacements predicted by reduced-order models for shroud degrees of freedom. In this study, some notable reduction of order methodologies based on substructuring, namely, fixed interface (Craig-Bampton), free interface (Rubin), and dual Craig-Bampton, and the mixed interface method, which is a combination of free and fixed interface methods, are investigated. The center of attention in this work is the modal contributions of components to the final result and the influence of modal characteristics of substructures on the efficiency of a particular reduction technique. To this end, the methods are examined by a different number of retained modes. The effect of adding up more vibration modes to the reduction basis on the accuracy and computational cost for each reduction technique is compared for predefined error tolerance. It is concluded that the physical characteristics of the blade and disk components significantly affect the forced response of the bladed disk system. Consequently, it can be capitalized on to find a more effective reduction technique for the specific geometry of shrouded blisks to address high computational cost and accurate forced response required in specific areas.