Reduced Order Modeling for Nonlinear Vibration Analysis of Mistuned Multi-Stage Bladed Disks with a Cracked Blade

Abstract

In this paper, a novel modeling methodology for the nonlinear vibration analysis of multi-stage bladed disk systems with small blade-to-blade mistuning and a cracked blade is proposed. The modeling strategy is based on an efficient stage-wise reduced order modeling method based on cyclic-symmetry analysis and component mode synthesis. Reduced order models are constructed for individual stages and assembled by projecting the motion of the interface of the neighboring stages onto a set of harmonic shape functions. The analysis procedure allows the stages to have different numbers of blades and mismatched computational grids on the interfaces of the neighboring stages. Furthermore, the modeling framework is independent of the modeling method for each stage, which enables the use of various existing modeling methods of single stages. Moreover, nonlinearity can also be included in the multi-stage computations, as long as the nonlinearity can be modeled for a single stage. To demonstrate the capability of the modeling procedure, the nonlinear effect of crack opening and closing is considered, in conjunction with the effects of small mistuning. The accuracy and efficiency of the proposed methods are discussed.