Probabilistic analysis of maximum mode shape for mistuned blisk

Abstract The high-fidelity finite element model (HFFEM) and Monte Carlo (MC) simulation of the blisk involve large number of calculations, which leads to low computational efficiency. In this case, an improved quasi-static mode compensation method (IQSMCM) and quadratic function-extremum response surface method (QF-ERSM) are proposed to investigate the probability distribution of mistuned blisk based on its vibration characteristics. The number of nodes and elements of IQSMCM relative to HFFEM are, respectively, reduced by 79.66 and 80.03%. Thus, the degrees of freedoms (DOFs) of IQSMCM are obviously reduced compared with that of HFFEM, and its computational efficiency is obviously increased. The maximum displacement shape (MDS) is investigated via IQSMCM. The computational efficiency is enhanced in the condition of ensuring the computational accuracy. Based on the investigation of maximum mode shape, the probability analysis is performed via QF-ERSM. The computational accuracy of QF-ERSM is improved by 93.80% compared with that of MC. Furthermore, the computational efficiency of QF-ERSM is higher 57.06% than that of QF-RSM. The sample history, extremum response surface function, sample history and distribution histogram of MDS are obtained via QF-ERSM, which provides an important guidance for the reliability research of the mistuned blisk. This research can be applied not only to aeroengine’s blisk but also to other large and complex mechanical structures in practical engineering.