This paper proposes a modeling method of rotating hard-coated drum-disk structures considering the strain-amplitude dependency of coatings and studies the veering of frequency curves and nonlinear coupled vibration. Firstly, Sanders’ shell theory and Kirchhoff's plate theory are used to derive the energy expressions of the hard-coated drum and hard-coated disk, respectively. The arbitrary multi-arc joints between disk and drum and arbitrary boundaries are presented based on the artificial spring. Furthermore, the displacements of the drum and disk are expanded by using the orthogonal polynomials, and Lagrange's equations are employed to derive the linear semi-analytical model. Secondly, the multi-domain dividing approach is used to develop a general method considering the strain-amplitude dependency in the rotation state, and the nonlinear semi-analytical model of rotating hard-coated drum-disk structures is created and further solved by an efficient algorithm proposed in the present work. The convergence and validation of the semi-analytical model are verified. Finally, the veering of frequency curves caused by the variations in rotation speeds, connection and boundary conditions, and thickness of coatings and substrates is revealed. The variation law and mechanism of nonlinear coupled vibration during veering are also investigated. The proposed modeling method can provide helpful references for the modeling and vibration analysis of multi-stage hard-coated drum-disk structures in aero-engine and other rotating hard-coated structures.

本文提出了一种考虑涂层应变幅度依赖性的旋转硬涂层鼓盘结构建模方法，并研究了频率曲线的转向和非线性耦合振动。首先，分别利用Sanders壳理论和Kirchhoff板理论推导了硬膜鼓和硬膜盘的能量表达式。提出了基于人工弹簧的圆盘与滚筒之间的任意多圆弧节点和任意边界。此外，利用正交多项式展开了磁鼓和圆盘的位移，并利用拉格朗日方程推导出了线性半解析模型。其次，使用多域划分方法开发了一种考虑旋转状态下应变幅度依赖性的通用方法，并且通过本工作中提出的有效算法创建并进一步解决了旋转硬涂层鼓盘结构的非线性半解析模型。验证了半解析模型的收敛性和有效性。最后，揭示了由转速、连接和边界条件以及涂层和基材厚度的变化引起的频率曲线的转向。研究了转向过程中非线性耦合振动的变化规律和机理。所提出的建模方法可为航空发动机等旋转硬涂层结构中多级硬涂层鼓盘结构的建模和振动分析提供有益的参考。