Rotating orthotropic blade equations based on the assumptions of the plate theory and the nonlinear von Kármán strain–displacement relations are obtained, and, furthermore, updated equations associated with prestressed configuration are provided. The extended Galerkin method is employed to determine the prestressed configuration due to the rotation and to obtain the linear frequencies and normal modes of updated equations. The multiple scales method, in combination with the Galerkin method, is used to study the nonlinear vibrations and to obtain analytical relations for the nonlinear frequencies and mode shapes. The role of different parameters on the backbone curves and effective nonlinearity coefficients is evaluated. In the nonlinear analysis, internal resonance is also considered. Moreover, the fourth-order Runge–Kutta method is applied to numerically analyze the nonlinear responses. A detailed investigation shows that in the torsion modes, the aspect ratio and the stiffness ratio changes influence the nonlinearity type and quality of the results. The quantities of effective nonlinearity coefficients depend on the rotational speed and the types of material and geometry. In the case of internal resonance, the stability of the nonlinear modes has been evaluated, and it is found that the rotating blades have different stable and unstable coupled modes.

获得了基于板理论和非线性 von Kármán 应变-位移关系的旋转正交各向异性叶片方程，此外，还提供了与预应力配置相关的更新方程。扩展伽辽金方法用于确定由于旋转而产生的预应力配置，并获得更新方程的线性频率和正常模式。多尺度法与伽辽金法相结合，用于研究非线性振动并获得非线性频率和模态振型的解析关系。评估了不同参数对骨干曲线和有效非线性系数的作用。在非线性分析中，还考虑了内部共振。而且，四阶 Runge-Kutta 方法用于数值分析非线性响应。详细研究表明，在扭转模式下，纵横比和刚度比的变化会影响结果的非线性类型和质量。有效非线性系数的数量取决于转速以及材料和几何形状的类型。在内部共振的情况下，对非线性模式的稳定性进行了评估，发现旋转叶片具有不同的稳定和不稳定耦合模式。有效非线性系数的数量取决于转速以及材料和几何形状的类型。在内部共振的情况下，对非线性模式的稳定性进行了评估，发现旋转叶片具有不同的稳定和不稳定耦合模式。有效非线性系数的数量取决于转速以及材料和几何形状的类型。在内部共振的情况下，对非线性模式的稳定性进行了评估，发现旋转叶片具有不同的稳定和不稳定耦合模式。