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研究生: 黃星諭
Huang, Hsing-Yu
論文名稱: 波浪與可變形板作用之數值模擬
Numerical Simulation of Wave Interaction with Deformable Plates
指導教授: 李兆芳
Lee, Jaw-Fang
學位類別: 碩士
Master
系所名稱: 工學院 - 水利及海洋工程學系
Department of Hydraulic & Ocean Engineering
論文出版年: 2017
畢業學年度: 105
語文別: 中文
論文頁數: 62
中文關鍵詞: 可變形板邊界元素法有限元素法
外文關鍵詞: deformable plates, boundary element method, finite element method
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  • 本研究求解二維波浪通過可變形板之問題,分別探討波浪與單一、兩列及多列可變形板之互制作用,對於波浪場的描述利用進行波理論,而可變形板的部分則是使用撓曲性樑理論,問題的計算上波浪場為利用邊界元素法,可變形板則使用有限元素法。分別求解出各個波浪場及各列可變形板之數值方法表示式後,即可合併各個表示式一同求解,最後求解出波浪場的勢函數及可變形板的位移量。
    在數值模式的驗證上,利用數學上的收斂性及系統的能量守恆觀點對模式進行驗證,說明數值模式的正確性後,分別對波浪與單一、兩列及多列可變形板作用進行討論,對於單一可變形板,其結果符合真實物理現象。在兩列可變形板的討論中,發現當兩列可變形板間距為0.1+0.5倍數波長時,共振現象會發生,另外當兩列可變形板的撓曲勁度越接近時,共振現象會越劇烈。最後發現在兩列可變形板後方會與第二列可變形板引起共振現象的距離放置一列可變形板,第一列與第二列之間距不會影響波浪場的反射係數及透過係數。

    The two-dimensional problems of the interaction between waves and one, two and a series of deformable plates are discussed in this study. The fluid motion is described by the linear wave theory. The deformable plates are simplified as the one-dimensional beams with uniform stiffness and mass distribution. A boundary element method is used to calculate the wave field. The Euler-Bernoulli beam theory is used to describe the motion of the deformable plate, which is calculated on the basis of a finite element method in combination with the BEM model. The numerical solutions are derived for the velocity potentials together with the displacements of the deformable plates.
    All of the numerical models meet the numerical convergence criterion and energy conservation. It demonstrates the correctness of the present numerical solution. Finally, the interaction between waves and one, two and a series of deformable plates are investigated. For one deformable plate, the numerical model presents the actual physical realities. For two deformable plates, resonance occurs when the interval between two deformable plates is equal to one-tenth wavelength plus a multiple of half-wavelength of the incident wave. Resonance is getting stronger when the flexural rigidities of two deformable plates are becoming closer. For a series of deformable plates, the reflection and transmission coefficients are not affected by the interval between the first and the second deformable plates as resonance occurs in the interval of the second and the third deformable plates.

    中文摘要 I Extended Abstract II 誌謝 IX 目錄 X 圖目錄 XII 符號說明 XIV 第一章 緒論 1 1-1 前言 1 1-2 文獻回顧 2 1-3 研究方法 3 1-4 本文架構 4 第二章 理論描述 5 2-1 問題之描述 5 2-2 可變形結構物之描述 9 第三章 數值模式 10 3-1 單一可變形板求解 10 3-1-1 第一區波浪場 11 3-1-2 第二區波浪場 12 3-1-3 單一可變形板 14 3-1-4 數值方法合併求解 16 3-2 兩列及多列可變形板求解 18 3-2-1 第一區波浪場 19 3-2-2 第二區波浪場 20 3-2-3 第三區波浪場 21 3-2-4 第一列可變形板 23 3-2-5 第二列可變形板 26 3-2-6 數值方法合併求解 28 3-3 反射係數及透過係數求解 30 第四章 結果與討論 32 4-1 單一可變形板數值模式之驗證及討論 32 4-2 兩列可變形板數值模式之驗證及討論 39 4-3 多列可變形板數值模式之驗證及討論 44 第五章 結論與建議 49 5-1 結論 49 5-2 建議 50 參考文獻 51 附錄A 可變形板有限元素法數值模式 53 附錄B 波浪場邊界元素法數值模式 60

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