Abstract A blade with an adjustable stagger angle is a type of blade that is able to partially rotate around its long axis. In fact, while a hub rotates, simultaneously the angle of the blade root section can change. The objective of this research is to develop and analyze a model of rotating cantilever orthotropic blade with adjustable stagger angle. Using Hamilton's principle, the governing partial differential equations are derived. In this formulation, both the Coriolis effects and centrifugal inertia forces are accounted for. First, the extended Galerkin method is utilized to discretize the equations of motion. Then, the multiple scales method is used to investigate the dynamic stability of the rotating blades analytically. Consequently, the possibility of internal resonances between different modes is studied and recognized. Moreover, the influence of various parameters on the instability regions is evaluated in detail, and the results are discussed. For validating the results, the modal characteristics of the system obtained by two methods of extended Galerkin and extended Kantorovich are compared with each other. Additionally, the fourth-order Runge–Kutta algorithm is employed to more deeply understand the dynamic behaviors of the system in the cases of constant and variable stagger angles and the differences between them as well as to prove the validity of the results of multiple scales method. The time histories, phase space diagrams and frequency spectrums are provided. Furthermore, a detailed investigation is carried out to determine the properties of the response under different conditions of the amplitude of the variable angle. As far as we know, the present study is the first attempt to demonstrate the effects of time-varying stagger angle for this class of problems in the literature. A stable motion in the adjustable stagger angle configuration gives a more complicated response. It can be observed that in this dynamic situation, the results are affected by Coriolis, both in quality and quantity. The findings indicate that with a change in the speed, there is a possibility of switching instability zones relative to each other. It is also found that the maximum width of the instability regions among the combination resonances is related to the second spanwise and first chordwise bending modes. The type of instability qualitatively depends on the amplitude of angle.

中文翻译：

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可调交错角旋转叶片的建模与动力学研究

摘要 交错角可调叶片是一种能绕其长轴部分旋转的叶片。事实上，当轮毂旋转时，同时叶根部分的角度会发生变化。本研究的目的是开发和分析具有可调交错角的旋转悬臂正交异性叶片模型。使用哈密顿原理，推导出控制偏微分方程。在这个公式中，科里奥利效应和离心惯性力都被考虑在内。首先，利用扩展伽辽金方法离散化运动方程。然后，采用多尺度方法对旋转叶片的动态稳定性进行解析研究。因此，研究并认识到了不同模式之间内部共振的可能性。而且，详细评估了各种参数对不稳定区域的影响，并对结果进行了讨论。为了验证结果，将通过扩展伽辽金和扩展康托罗维奇两种方法获得的系统的模态特性相互比较。此外，采用四阶Runge-Kutta算法更深入地了解系统在恒定和可变交错角情况下的动态行为及其差异，并证明多尺度方法结果的有效性. 提供了时间历程、相空间图和频谱。此外，还进行了详细的研究，以确定在可变角度幅度的不同条件下的响应特性。据我们所知，本研究是首次尝试证明时变交错角对文献中此类问题的影响。可调交错角配置中的稳定运动提供更复杂的响应。可以观察到，在这种动态情况下，结果在质量和数量上都受到科里奥利的影响。研究结果表明，随着速度的变化，有可能相对于彼此切换不稳定区域。还发现组合共振中不稳定区域的最大宽度与第二展向和第一弦向弯曲模式有关。不稳定性的类型定性地取决于角度的幅度。可调交错角配置中的稳定运动提供更复杂的响应。可以观察到，在这种动态情况下，结果在质量和数量上都受到科里奥利的影响。研究结果表明，随着速度的变化，有可能相对于彼此切换不稳定区域。还发现组合共振中不稳定区域的最大宽度与第二展向和第一弦向弯曲模式有关。不稳定性的类型定性地取决于角度的幅度。可调交错角配置中的稳定运动提供更复杂的响应。可以观察到，在这种动态情况下，结果在质量和数量上都受到科里奥利的影响。研究结果表明，随着速度的变化，有可能相对于彼此切换不稳定区域。还发现组合共振中不稳定区域的最大宽度与第二展向和第一弦向弯曲模式有关。不稳定性的类型定性地取决于角度的幅度。存在相互切换不稳定区域的可能性。还发现组合共振中不稳定区域的最大宽度与第二展向和第一弦向弯曲模式有关。不稳定性的类型定性地取决于角度的幅度。存在相互切换不稳定区域的可能性。还发现组合共振中不稳定区域的最大宽度与第二展向和第一弦向弯曲模式有关。不稳定性的类型定性地取决于角度的幅度。