本研究旨在發展二維非線性數值水槽，用以探討非線性波浪作用下，浮式結構物上方水箱內的液體震盪現象，及此現象所引發的結構物動力特性。基於勢能理論的假設下，採用邊界元素法發展數值模式，模擬波浪場中裝載液體之雙胴浮式平台的動力特性，包括sway、heave、roll和張力反應，同時執行水工模型試驗來驗證數值模式之正確性。
數值模式中，邊界積分方程式由線性元素進行離散，非線性自由液面則採用Mixed Eulerian and Lagrangian (MEL) 法搭配Runge-Kutta fourth-order (RK4) 法和cubic spline scheme處理，造波邊界條件則採用Stokes二階解析解給定，數值水槽前後兩端皆設置消波區以消除波浪通過結構物所產生的反射波和透射波。而平台運動方程式則由加速勢法和模態分解法(modal decomposition method) 得到Φ1,t和Φ2,t後，再利用unsteady Bernoulli equation和Newton's 2nd law求得，最後再由RK4計算下一時刻平台重心的位移和速度，以及自由液面的位置和流速勢。實驗驗證方法上，是以高速攝影機拍攝平台的運動和水箱內液面變化，再利用影像處理技巧分析平台的運動軌跡，而錨碇纜繩張力量測部分則使用張力計記錄張力變化。
數值模式與水工模型試驗結果比較顯示，在共振頻率附近，受到黏性效應的影響，數值模式會有高估的情況，因此為降低黏性效應的影響，並且在不影響計算效率的考量下，本研究在數值模式中加入非耦合的阻尼係數矩陣，此阻尼係數由阻尼比來表示，結果發現當阻尼比設定為ζ=0.02時，結構物各自由度共振頻率附近的運動反應有明顯的降低，而其餘範圍則無明顯改變，此結果使得數值計算結果與實驗值更接近，因此本研究之結構物適合之阻尼比設定為ζ=0.02。
本研究應用加入阻尼係數後的數值模式，探討改變幾種條件對於浮式平台動力特性的影響，包括錨碇彈簧係數、錨碇角度、平台跨距以及水箱條件。結果顯示，改變上述條件都可能造成平台運動與錨碇張力反應的共振頻率偏移以及反應大小的改變。整體而言，錨碇角度較小、平台跨距較大、水箱內液體較高以及水箱寬度較寬情況下，浮式平台運動的較為平穩，其所受錨碇張力也較小。
結構物在不規則波與規則波之運動反應比較方面，整體而言，不規則波作用下浮式結構物的水箱內液體變化較混亂，因而造成浮式結構物各項運動產生互制之抵消作用，使得浮式結構物運動有轉趨平緩之趨勢。
關鍵詞：邊界元素法、非線性數值水槽、雙胴浮式結構物

This study is to develop a 2D fully nonlinear numerical wave tank used to investigate the wave-induced dynamic properties of a dual pontoon floating structure (DPFS) with a liquid container on the top. The nonlinear numerical wave tank, developed based on the velocity potential function and the boundary element method (BEM), is to simulate dynamic properties including sway, heave, roll, and tension response. In addition, a physical model of the dual floating pontoon is tested in a hydrodynamic wave tank to validate the numerical model for simulation of wave and structure interaction.
In the numerical model, a boundary integral equation method (BIEM) with linear element scheme is applied to establish a 2D fully nonlinear numerical wave tank (NWT). The nonlinear free surface condition is treated by combining the Mixed Eulerian and Lagrangian method (MEL), the fourth-order Runge-Kutta method (RK4) and a cubic spline scheme. The second-order Stokes wave theory is used to generate the velocity flux on the input boundary. Numerical damping zones are deployed at both ends of the NWT to dissipate or absorb the transmitted and reflected waves. Acceleration potential method and modal decomposition method are adopted to solve the unsteady potential functions Φ1,t and Φ2,t, while the system of motion equation is established according to Newton's 2nd law. Finally, the RK4 is applied to predict the motion of the platform, and the variation of free surface. As for the hydrodynamic laboratory model test, an image process scheme is applied to trace the floating structure motion and the variation of water surface inside the sloshing tank, while the mooring tension is measured by a load cell and stored in a data logger.
The comparisons of numerical simulations and experimental data indicate that the numerical predictions are larger than measurements especially near the resonance frequency. This discrepancy is probably due to the fluid viscous effect. To overcome this problem and maintain the calculation efficiency, an uncoupled damping coefficient obtained through a damping ratio (ζ=C/Ccr=0.02) is incorporated into the vibration system. Results reveal that responses of body motion near the resonant frequencies of each mode have significantly reduced and close to the measurements. Therefore, the suitable value of the damping ratio for the floating platform is ζ=0.02.
Then the numerical model with a damping ratio is applied to investigate the dynamic properties of the floating platform for different arrangements, including different mooring angle, spring constant, spacing, and the liquid container. Results demonstrate that the resonant frequency of each mode, responses of body motion and mooring tensions change along with the settings. As a whole, the platform with smaller mooring angle, longer spacing between the pontoons, higher water depth and wider width of the liquid container has relatively stable body motions and less mooring tension.
Finally, the comparisons of the effects of random and regular waves on the floating structure illustrate that the variation of water surface in the liquid container is much severe in random waves than in regular waves such that the interaction between liquid and floating structure is more chaotic and thus reduces the amplitude of each response mode. As a result, the mooring tensions for random waves become much gentler than the regular waves.
Key words: Boundary integral equation method; fully nonlinear numerical wave tank; dual pontoon floating structure

中文摘要 i
英文摘要 iii
目錄 v
圖目錄 ix
表目錄 xiii
符號對照表 xv
第一章 緒論 1
1.1 研究動機與目的 1
1.2 文獻回顧 1
1.3 研究目的 2
1.4 研究方法 3
1.5 文章架構 3
第二章 理論基礎 5
2.1 二維數值水槽 5
2.1.1 控制方程式 6
2.1.2 邊界積分方程式 6
2.2 邊界條件 7
2.2.1 計算領域 之邊界條件 7
2.2.2 計算領域 之邊界條件 10
2.3 波浪作用在結構物上的外力和力矩 11
2.4 加速勢法 11
2.5 模態分解法 13
2.6 錨碇系統 16
2.7 含阻尼效應的自由振動系統 18
第三章 數值方法 19
3.1 曲線座標系統 19
3.2 自由液面與固體交界面速度修正 20
3.3 The 4th-order Runge-Kutta method 21
3.4 網格重置 21
3.5 自由液面平滑化 22
第四章 水工模型實驗 23
4.1 實驗目的 23
4.2 實驗模型尺寸及材質 23
4.3 實驗儀器與設備 24
4.4 量測項目 28
4.5 實驗佈置 29
4.6 實驗步驟 29
4.7 分析方法 32
4.7.1 張力分析 32
4.7.2 平台剛體運動分析 33
第五章 結果與討論 37
5.1 數值模式與實驗結果比較 37
5.2 數值模式應用 42
5.2.1 入射波高的影響 43
5.2.2 水箱的影響 46
5.2.2.1水箱內液體高度的影響(case 1, case 2, case 3) 47
5.2.2.2水箱寬度的影響(case 1, case 2, case 4) 50
5.2.3 水深的影響 54
5.2.4 錨碇角度的影響 58
5.2.5 平台跨距的影響 62
第六章 結論與建議 67
6.1 結論 67
6.2 建議 68
參考文獻 71
附錄A 結構物運動及邊界條件 75
附錄B 質量慣性矩 81
附錄C 反射率計算 85
附錄D 不規則波案例 89

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