本研究是考慮近海風場風機塔柱受多重外力產生振動時，嘗試利用兩個減振環 (Damping rings)，分析其對於風機塔柱之減振效益。本研究以3D 非線性 fixed-free elastic beam 模擬風機塔柱之橫向及側向振動情況。吾人考慮的外力為：迎風向 (y-dir) 的空氣阻力，側向 (z-dir) 的空氣力，以及迎風向彈性樑自由端 (tip free end) 的風機所施予之點受力；另外還考慮海面下的 y-dir 洋流外力。我們將以非穩態之外力函數模擬這些流場 (包含洋流及氣流) 對於塔柱造成的分佈力。基於流場流速之改變，其相對之塔柱形變量也改變，而導致整個塔柱受力也產生變化，這將形成一典型的氣體彈性問題。值得注意的是本研究僅限於塔柱之振動問題，對於一般風機葉片的空氣動力的分析並非本文重點，而風機施於塔柱端點力僅以一單純的時變外力模擬之。此外，由於彈性樑端點受力的情況將導致此彈性樑邊界條件的改變，此問題可視同一時變的邊界條件問題 (time-dependent boundary condition)。吾人將利用Mindlin-Goodman之轉換方法，求出塔柱端點受力之橫向振動模態 (mode shape) 的解析函數。與其他各種外力結合後，利用時間多尺度法 (method of multiple scales (MOMS)) 分析此非線性的問題。值得注意的是此 3D elastic beam 除了受多重外力而導致的振動問題外；由於其截面的對稱性，將會導致 y-dir 及 z-dir 的模態及自然振動頻率一樣，因此會有非線性橫樑特有之 1:1 內共振現象 (1:1 internal resonance)。準此，吾人使用兩減振環裝設於風機塔柱上，探討此兩環之相對位置、質量及彈性係數，以達到避開內共振，並有最佳之減振效果。吾人希望此設計能適用一般風機之減振，即使風機塔柱自然頻率和外力頻率相近產生共振時，也不會產生很大的形變量，此研究有助於台灣近海風機塔柱減振之參考。 Beams are widely applied in engineering, such as wings in aerospace, bridges in civil engineering, and train rails in mechanical engineering. In these applications, the fatigue and failure caused by vibrations in beam members tend to receive the most attention from engineers. This study investigated the damping effects of two Damping Rings (DRs) on a wind turbine tower (considered as a fixed-free 3D nonlinear beam) with existing internal resonance. This wind turbine tower was subjected to multi external forces: (1) the time dependent force applied on the beam tip (considered as the wind turbine force on the tower), (2) the wind force directly applied on the beam and its associated aerodynamic force on the side of the beam, and (3) the ocean wave force applied under the sea level and its associated wake force applied on the side of the beam under sea level. Only the beam vibration reduction is considered, neither the aerodynamic force formulation of the wind turbine blade nor the wind turbine effects are not the main concern of this study. We applied the Mindlin-Goodman method to find the mode shape of this time-dependent boundary beam. We analyzed this nonlinear system using the method of multiple scales (MOMS). Fixed points plots were also used to facilitate the observation of internal resonance. This made it possible for us to study the influence of nonlinear vibrations of the elastic beam. The 1:1 internal resonance was found in the y- and z- dir. of the system. This prompted us to add 2 DRs (damping rings) on the elastic beam in order to suppress internal resonance and vibrations. We examined the influence of the mass and location of the DRs as well as damping and spring coefficients on the damping effects. Analysis data were presented in graphs, including 3D maximum amplitude plots of the modes and 3D maximum amplitude contour plots (3D MACPs). As far as we know, no previous study has employed combinations of this type of damping rings to wind turbine towers. Our approach to damping is comprehensive in practical applications.
