異向性材料薄壁懸臂梁之振動分析

Abstract

近年來，風力發電機葉片逐漸傾向尺寸加長且輕量化的設計方向發展。然而，這可能導致更劇烈的振動，甚至引發顫振（flutter）現象並加劇材料疲勞的問題，對風力發電機的可靠性和壽命造成嚴重影響。本研究旨在建立一高可信度的一維薄壁梁（thin-walled beam, TWB）模型，以應用於層板葉片在受風時之振動分析，從而改進風力發電機的設計和性能。本研究首先採用簡易的矩形空心薄壁梁模型，通過該模型並利用其幾何特性，對梁的應力狀態進行簡化，並且考慮多自由度的耦合運動。透過哈密頓原理，推導包含梁彎曲、扭轉和拉伸之運動方程式。層板之材料選取單向纖維強化的型式，此材料具有橫向等向性，並設置一可調節的層角，進一步探討一個簡易的單層板矩形截面懸臂梁之案例，並建立各自由度之等效質量與勁度參數。接著採用延伸加勒金方法（extended Galerkin method）對各參數於自由振動時沿著軸向之模型和對應的自然頻率進行求解，並對所獲得之數值結果進行一系列的驗證。結果顯示，自然模態勁度不受層角方向的影響。然而，耦合模態勁度、模態振型和自然頻率則受到層角方向的顯著影響。層角方向還可以決定解耦現象的發生，使多自由度耦合模態轉變為自然模態。此外，研究結果還表明，自然頻率隨著層角的增加而增大。本研究成果預期為複合材料葉片振動與顫振分析提供可靠的模型基礎。未來可以再進一步擴展研究範圍，考慮更複雜的葉片幾何結構，並引入風誘發負載。由於TWB計算之成本低且具有高可信度的特點，增進與大型且複雜之紊流風場模擬相結合之可行性，以更精確地評估大型風力發電機葉片之疲勞效應和性能表現。

In recent years, there has been a trend towards the elongation and lightweight design of wind turbine blades. However, this may result in more intense vibrations, potentially causing flutter phenomena and exacerbating material fatigue issues, significantly impacting the reliability and lifespan of wind turbines. This study aims to establish a highly reliable one-dimensional thin-walled beam (TWB) model for the vibration analysis of laminate blades under wind loading, thereby improving the design and performance of wind turbines. Initially, this study employs a simple rectangular hollow thin-walled beam model. Utilizing the geometric properties of the model, the stress state of the beam could be simplified and the coupling motion of multi-degree of freedom could be considered. Through the Hamilton's principle, the equations of motion including bending, twist, and extension of the beam could be derived. The laminate material was selected to be unidirectional fiber-reinforced, possessing transverse isotropy, with an adjustable ply angle. A simplified case of a single-layer rectangular cantilever beam was then investigated and the equivalent mass and stiffness quantities for each degree of freedom was established. Subsequently, the extended Galerkin method was employed to solve for the mode shapes and corresponding natural frequencies along the axial direction under free vibration, followed by a series of verifications of the numerical results obtained. The results indicate that the natural stiffness quantities remain unaffected by the orientations of the ply angles. However, the coupling stiffness quantities, mode shapes, and natural frequencies are significantly influenced by the orientations of the ply angles. The ply angle orientations can also determine the occurrence of decoupling phenomena, causing multi-degree of freedom coupling modes to transform into natural modes. Additionally, the findings demonstrate that natural frequencies generally increase with the ply angle. The outcomes of this research are expected to provide a reliable foundation for vibration and flutter analysis of composite material blades. Future research may expand to consider more complex blade geometries and introduce wind-induced loading. Leveraging the low computational cost and high reliability of TWB, enhancing the feasibility of integration with large and complex turbulent wind field simulations will enable more accurate assessments of fatigue effects and performance of large-scale wind turbine blades.