Hard coatings have been used to reduce the vibration levels of blisks in several studies. In the design process, coating-geometric mistuning and blade-substrate multi-mistuning are inevitable; and even the coatings have material nonlinearity. However, this type of complicated blisk had never been studied previously. In this paper, a graded modeling method is presented to model the blisks with coating-geometric mistuning, blade-substrate multi-mistuning, and coating-material nonlinearity, where three reduction steps and a modified subspace iterative (MSI) method are developed to improve computational efficiency and accuracy. Several numerical analyses are performed to validate the developed models. The results indicate that for coated blisks with the aforementioned mistuning factors and material nonlinearity, the MSI-based reduced-order models (ROMs) have higher computational efficiency than the Craig–Bampton-based ROMs and full models, and they have higher computational accuracy than the frequency-based ROMs.

在多项研究中，硬涂层已被用于降低叶盘的振动水平。在设计过程中，涂层-几何错位和叶片-基板多错位在所难免；甚至涂层具有材料非线性。然而，这种复杂的叶盘以前从未被研究过。在本文中，提出了一种分级建模方法来对具有涂层几何失谐、叶片衬底多失谐和涂层材料非线性的叶盘进行建模，其中开发了三个缩减步骤和一种改进的子空间迭代 (MSI) 方法来改进计算效率和准确性。进行了若干数值分析以验证开发的模型。结果表明，对于具有上述失谐因素和材料非线性的涂层叶盘，