Reduced Order Models for Largely Mistuned Blisks with Small Random Mistuning

Mistuning can break the cyclic symmetry of an ideally tuned blisk and cause its forced response to increase drastically. In the absence of cyclic symmetry, the finite element method (FEM) requires a vast amount of computational costs for predicting the dynamic characteristics of mistuned systems. To greatly reduce the computational costs of FEM, various reduced-order models (ROMs) have been developed. However, most existing ROMs are only effective for small mistuning or large mistuning situations. To resolve more complicated mistuning problems, this paper proposes two new approaches for blisks with both small mistuning and large mistuning. The first method extends the idea of the subset of nominal modes (SNM), in which modes of a largely mistuned system with small mistuning can be represented in terms of a subset of the pseudo-nominal system modes (SPNM). Because SPNM has to use system-level modes and calculation, the second method, called remaining damaged interface decomposition (HRDID), is further proposed, which is based on the basic principle of SPNM. It requires only sector-level modes and calculation. Furthermore, SPNM, HRDID, and FEM are used separately to calculate both the natural frequencies and mode shapes of mistuned academic blisks. The results of SPNM and HRDID are compared separately with those calculated by FEM to verify their accuracy. Finally, statistical analysis is performed to investigate the effect of random mistuning on a pseudo-nominal system.