Nonlinear cyclic reduction for the analysis of mistuned cyclic systems
Résumé
Predicting the vibratory response of bladed-disks in turbomachinery is of the utmost importance to design a reliable and optimized engine. Yet, such simulations are challenging mainly due to the large size of the finite-element model used to describe the system, the existence of random mistuning coming from manufacture tolerances, and the nonlinear effects arising from the different components and their coupling. As a consequence, very few reduced-order models handling nonlinear mistuned systems have yet been proposed and the existing ones try to find the best compromise between a computationally efficient simulation and a correct description of the nonlinear phenomena. In this paper, a novel approach is proposed to tackle this challenge. Its key ideas rely on the substructuring concept and the cyclic properties of the structure. A reduction basis composed of cyclic complex nonlinear normal modes is created on each sector of the system leading to a compact nonlinear superelement per sector. The system is then assembled and a synthesis simulation is performed. Due to the main concepts employed, the method is referred to as the Substructuring method based on Nonlinear Cyclic Reduction (SNCR). It is validated on a finite element model of a tuned, a randomly mistuned and an intentionally mistuned bladed-disks. It will be shown to be fast and accurate despite strong nonlinearities. Due to its flexibility and efficiency, the method is expected to have a wide range of possible applications within the community.
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