Due to strong nonlinear, unsteady characteristics and the fluid–structure interaction effect, vibration analysis of blades under the excitation of the airflow is still one of the technical difficulties. In this paper, the accurate subsonic aerodynamic force is obtained through numerical simulation, and the aerodynamic coupling model of the rotary blade is established. The distribution of the aerodynamic force of the compressor blade under the unsteady airflow is focused on. The blade is modeled as presetting a presetting pre-twisted rotary cantilever plate. Dynamic frequencies of the plate, calculated by Chebyshev–Ritz method, are compared with frequencies calculated using the finite element method (FEM). Effects of different parameters on natural frequencies of the rotary plate are discussed. Based on von-Karman nonlinear geometric relation and the first-order shear deformation theory, nonlinear dynamic equations of the pre-twisted rotary plate under the combination of the centrifugal force and the aerodynamic are derived by utilizing Hamilton’s principle. Second-order ordinary differential equations are derived by applying the Galerkin method. Analytical solution of the dynamic deformation of the plate is presented and is compared with that produced by FEM. Results indicate the accuracy of the explicit presentation of the aerodynamic of the low-pressure compressor blade. Effects of the rotary speed, the thickness, the pre-twisted angle and the presetting angle on vibration characteristics of the warping blade are studied. Mode shape shift and frequency loci veering are discussed.

中文翻译：

---

亚音速气流联合激励下旋转板的线性振动

由于强非线性、非定常特性和流固耦合效应，气流激励下叶片的振动分析仍然是技术难点之一。本文通过数值模拟得到了精确的亚音速气动力，建立了旋翼的气动耦合模型。重点研究了非定常气流下压气机叶片的气动力分布。叶片被建模为预置预扭旋转悬臂板。将通过 Chebyshev-Ritz 方法计算的板的动态频率与使用有限元方法 (FEM) 计算的频率进行比较。讨论了不同参数对转盘固有频率的影响。基于von-Karman非线性几何关系和一阶剪切变形理论，利用Hamilton原理，推导了离心力和气动共同作用下预扭转盘的非线性动力学方程。二阶常微分方程是通过应用 Galerkin 方法导出的。给出了板的动态变形的解析解，并与有限元法产生的解析解进行了比较。结果表明了低压压气机叶片空气动力学的明确表示的准确性。研究了转速、厚度、预捻角和预置角对整经叶片振动特性的影响。讨论了模式形状偏移和频率定位。利用Hamilton原理，推导了离心力和气动共同作用下预扭转盘的非线性动力学方程。二阶常微分方程是通过应用 Galerkin 方法导出的。给出了板的动态变形的解析解，并与有限元法产生的解析解进行了比较。结果表明了低压压气机叶片空气动力学的明确表示的准确性。研究了转速、厚度、预捻角和预置角对整经叶片振动特性的影响。讨论了模式形状偏移和频率定位。利用Hamilton原理，推导了离心力和气动共同作用下预扭转盘的非线性动力学方程。二阶常微分方程是通过应用 Galerkin 方法导出的。给出了板的动态变形的解析解，并与有限元法产生的解析解进行了比较。结果表明了低压压气机叶片空气动力学的明确表示的准确性。研究了转速、厚度、预捻角和预置角对整经叶片振动特性的影响。讨论了模式形状偏移和频率定位。