Structures such as turbomachinery blades, industrial fans, propellers, etc. can be modeled as twisted beams. The study of dynamics of these structures is vital as operational failure of such structures can have catastrophic consequences. As the inclusion of twist and rotation complicates the problem, Finite Element (FE) method is widely used to determine the modal characteristics of rotating twisted beams. In this work, a novel formula is derived to estimate the natural frequencies of rotating twisted beams. The formula is derived using the perturbation method. The twist angle and the rotating speed are treated as the perturbation parameters. In general, the dynamics of rotating twisted beams is coupled in the two transverse planes. However, in the first part of the work the problem is assumed to be uncoupled and it is shown that this assumption is valid under certain cases. In the second part, the problem of general coupled dynamics is solved. Interesting insights based on the formula are presented. The accuracy of the derived formula is verified by comparing it with the literature and FE simulation results. It has been shown that the formula is valid over a fairly large range of twist angles and rotating speeds. In contrast to the detailed FE simulation, the derived analytical formula will be better suited for design iterations in industrial practice.

中文翻译：

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旋转扭曲梁的固有频率：一种基于微扰方法的方法

涡轮机械叶片、工业风扇、螺旋桨等结构可以建模为扭曲梁。研究这些结构的动力学至关重要，因为这些结构的操作故障可能会带来灾难性的后果。由于包含扭曲和旋转使问题复杂化，有限元 (FE) 方法被广泛用于确定旋转扭曲梁的模态特性。在这项工作中，推导出了一个新的公式来估计旋转扭曲梁的固有频率。该公式是使用扰动方法推导出来的。扭转角和转速被视为扰动参数。通常，旋转扭曲梁的动力学在两个横向平面中耦合。然而，在工作的第一部分中，假设问题是解耦的，并且表明该假设在某些情况下是有效的。第二部分解决了一般耦合动力学问题。提出了基于公式的有趣见解。通过与文献和有限元模拟结果的比较，验证了推导公式的准确性。已经表明，该公式在相当大的扭转角和转速范围内是有效的。与详细的有限元模拟相比，导出的分析公式将更适合工业实践中的设计迭代。通过与文献和有限元模拟结果的比较，验证了推导公式的准确性。已经表明，该公式在相当大的扭转角和转速范围内是有效的。与详细的有限元模拟相比，导出的分析公式将更适合工业实践中的设计迭代。通过与文献和有限元模拟结果的比较，验证了推导公式的准确性。已经表明，该公式在相当大的扭转角和转速范围内是有效的。与详细的有限元模拟相比，导出的分析公式将更适合工业实践中的设计迭代。