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Analysis of Structural Vibrations of Vertical Axis Wind Turbine Blades via Hamilton’s Principle — Part 2: Exact and Approximate Solutions
International Journal of Structural Stability and Dynamics ( IF 3.6 ) Pub Date : 2020-06-05 , DOI: 10.1142/s0219455420500996
Jianyou Huang, Chia-Ou Chang, Chien-Cheng Chang

In this part 2, we provide a detailed solution to the beam equations derived in Part 1 for a VAWT blade. The main results have been outlined in the abstract of Part 1 which includes the effects of various geometrical and physical parameters such as blade length [Formula: see text], chord length [Formula: see text], radius [Formula: see text] and angular speed [Formula: see text] as well as material damping [Formula: see text]. It is shown that among the four dimensions of deformation lateral bending is the dominant factor in determining the natural frequencies of the blade. In case the blade is rotating with a constant angular speed, the dispersion relation of the 1 degree-of-freedom (DOF) motion for lateral bending can be exactly derived that an implicit function of the natural, i.e. resonant frequencies has to be solved by a root-finding method. The mode shape function is then explicitly obtained. In particular, the natural frequencies of the 1-DOF motion for the rotating blade are shown to be conveniently approximated by simple analytical formulas in terms of those for the stationary blade and the angular speed of rotation. The dependence of the natural frequencies on the chord length can also be approximated analytically by a ratio formula for given blade length to chord ratio. In addition, resonance maps of natural frequency plotted versus various parameters are provided to fully exploit the usefulness of the main results. Through a series of analysis of 2-DOF systems, we show the respective importance of the centrifugal force, coupling deformation and the Coriolis force in modifying the natural frequencies of the 1-DOF model rather than simply ignoring any of these effects.

中文翻译:

通过汉密尔顿原理分析垂直轴风力涡轮机叶片的结构振动 — 第 2 部分:精确解和近似解

在这第 2 部分中,我们为第 1 部分中导出的 VAWT 叶片的梁方程提供了详细的解决方案。主要结果已在第 1 部分的摘要中进行了概述,其中包括各种几何和物理参数的影响,例如叶片长度 [公式:参见文本]、弦长 [公式:参见文本]、半径 [公式:参见文本] 和角速度[公式:见文本]以及材料阻尼[公式:见文本]。结果表明,在变形的四个维度中,横向弯曲是决定叶片固有频率的主要因素。在叶片以恒定角速度旋转的情况下,可以精确推导出横向弯曲的 1 自由度 (DOF) 运动的色散关系,即自然的隐式函数,即共振频率必须由下式求解一种寻根方法。然后显式获得振型函数。特别是,旋转叶片的 1-DOF 运动的固有频率可以方便地通过简单的解析公式来近似,这些公式就固定叶片和旋转角速度而言。固有频率对弦长的依赖性也可以通过给定叶片长度与弦长比的比率公式解析近似。此外,还提供了绘制的固有频率与各种参数的共振图,以充分利用主要结果的有用性。通过对 2-DOF 系统的一系列分析,我们展示了离心力、耦合变形和科里奥利力在修改 1-DOF 模型的固有频率方面的各自重要性,而不是简单地忽略任何这些影响。
更新日期:2020-06-05
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