On a New Nonlinear Reduced-Order Model for Capturing Internal Resonances in Intentionally Mistuned Cyclic Structures

Abstract

Cyclic structures such as turbomachinery present material and geometrical variations between sectors. These discrepancies are called mistuning and break the cyclic symmetry of the structure. Computing the forced response of mistuned cyclic structures is thus a numerical challenge. The component nonlinear complex mode synthesis (CNCMS) is one of the few nonlinear reduced-order model (ROM) formulations that allow to compute the nonlinear response of tuned and mistuned structures. It has been validated successfully for friction problems. However, in the presence of geometric nonlinearities, internal resonances may arise and they cannot be captured correctly with the CNCMS method. The purpose of this work is therefore to present a new methodology for developing a nonlinear ROM that can successfully capture internal resonances for tuned and mistuned structures. This method, called component mode synthesis with nonlinear reevaluation (CMSNR), is based on a variation of the CNCMS approach. The final modal synthesis uses a multiharmonic procedure and a reevaluation of the nonlinear forces on each sector independently. The performance and limitations of the proposed approach are assessed using a simplified example of a blisk subject to polynomial nonlinearities. Different internal resonances are exhibited and studied depending on the type of excitation force and on the level of mistuning.