Relative cyclic component mode synthesis: A reduced order modeling approach for mistuned bladed disks with friction interfaces

A new reduced order modeling technique for nonlinear dynamics of mistuned bladed disks with friction interfaces is presented. Although various models have been developed to characterize the dynamics of either mistuned or frictionally damped structures, predicting the vibratory response of mistuned bladed disks with frictional interfaces remains challenging due to the: large size of refined industrial models, nonsmooth friction nonlinearities and amplitude dependent dynamics, and lack of cyclic symmetry properties. The Relative Cyclic Component Mode Synthesis (RCCMS) approach benefits from the application of relative coordinates prior to performing a reduction. Based on the new method, the kinematics of contact surfaces are first described in terms of relative displacements between contact node pairs, afterwards the Craig-Bampton Component Mode Synthesis (CB-CMS) technique is employed to reduce the model size. Implementation of relative coordinates halves the number of nonlinear unknowns in the reduced space and enhances the CB-CMS reduction basis by incorporating system-level stick modeshapes. The proposed approach admits introduction of either blade or sector frequency mistuning into the final reduced order model. In this way, the reduction is performed only once, which makes it favorable for statistical analyses. In addition, the mistuned ROM can be developed with minimal computational effort by using the sector model only. The developed RCCMS-based ROM is demonstrated on a finite element model of a mistuned bladed disk with blade-root friction damping. Numerical simulations reveal the excellent accuracy in predicting the nonlinear forced response.