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研究生:徐銘賸
研究生(外文):Ming-Sheng Hsu
論文名稱:地表截切半橢圓形不連續引致的平面SH波散射及繞射
論文名稱(外文):Scattering and Diffraction of Plane SH Waves by Surface Truncated Semi-elliptic Discontinuities
指導教授:曹登皓曹登皓引用關係
指導教授(外文):Deng-How Tsaur
學位類別:博士
校院名稱:國立臺灣海洋大學
系所名稱:河海工程學系
學門:工程學門
學類:河海工程學類
論文種類:學術論文
論文出版年:2013
畢業學年度:101
語文別:中文
論文頁數:151
中文關鍵詞:水平剪力波散射繞射截切半橢圓形山谷部分填滿半橢圓形沉積山谷
外文關鍵詞:SH wavesscatteringdiffractiontruncated semi-elliptic canyonpartially filled semi-elliptic alluvial valley
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回顧過往的研究,水平剪力波的散射和繞射問題雖已被大量的研究過。然而,從數學的觀點來看,即使是一些簡單的幾何形狀,它們的解析解仍是不易獲得。在這樣的情況下,倘若其半解析解可被建立求得,也許能夠填補缺少解析解的遺憾。因此,本文利用領域選點媒親技巧,針對地表有截切半橢圓形不連續引致平面水平剪力波的散射及繞射問題,推求其半解析解,所謂的截切半橢圓形不連續包括:截切淺半橢圓形山谷、部分填滿淺半橢圓形沉積山谷、截切深半橢圓形山谷、部分填滿深半橢圓形沉積山谷等四種。求解程序的成功,決定於兩個關鍵點,即適當地挑選輔助邊界,以及利用不同橢圓座標系統之間的轉換關係式,來代替使用加法定理變換不同座標系統。輔助邊界將整個分析領域劃分成兩個子領域,並使波函數展開可應用至各子領域;座標轉換關係式則是實現必要的座標轉換。在本論文中,頻率域及時間域的反應皆被計算與討論,而所推導得到的截切半橢圓形山谷及部分填滿半橢圓形沉積山谷的半解析解,可計算模擬截切半圓形山谷及部分填滿半圓形沉積山谷等兩種情況,這使得本論文的結果更具一般性。本論文的計算結果,亦能夠提供給其它的數值方法作驗証比對的基準。最後,這裡所推薦的處理方式,也可以擴展至一些平面水平剪力波的散射與繞射問題,例如多個不連續地形的問題。
中文摘要
英文摘要
目錄
圖目錄
第一章 緒論
1-1 研究背景
1-2 文獻回顧
1-3 研究動機
1-4 研究目標與範圍
1-5 研究方法
1-6 研究內容及架構
第二章 彈性體中剪切波的波動方程
2-1 引言
2-2 彈性波的波動方程
2-3 控制方程的建立
第三章 截切淺半橢圓形山谷的散射與繞射
3-1 引言
3-2 理論公式
3-2-1 模型描述與邊界條件
3-2-2 波函數展開與求解
3-3 數值結果與討論
3-3-1 收斂測試
3-3-2 極限例的驗證
3-3-3 頻率域的地表反應
3-3-4 時間域的地表反應
第四章 部分填滿淺半橢圓形沉積山谷的散射與繞射
4-1 引言
4-2 理論公式
4-2-1 模型描述與邊界條件
4-2-2 波函數展開與求解
4-3 數值結果與討論
4-3-1 收斂測試
4-3-2 極限例的驗證
4-3-3 頻率域的地表反應
4-3-4 時間域的地表反應
第五章 截切深半橢圓形山谷的散射與繞射
5-1 引言
5-2 理論公式
5-2-1 模型描述與邊界條件
5-2-2 波函數展開與求解
5-3 數值結果與討論
5-3-1 收斂測試
5-3-2 極限例的驗證
5-3-3 頻率域的地表反應
5-3-4 時間域的地表反應
第六章 部分填滿深半橢圓形沉積山谷的散射與繞射
6-1 引言
6-2 理論公式
6-2-1 模型描述與邊界條件
6-2-2 波函數展開與求解
6-3 數值結果與討論
6-3-1 收斂測試
6-3-2 極限例的驗證
6-3-3 頻率域的地表反應
6-3-4 時間域的地表反應
第七章 結論與未來展望
7-1 結論
7-2 未來展望
參考文獻
附錄
附錄A 第三章聯立式自定函數的整理
附錄B 第四章聯立式自定函數的整理
附錄C 第五章聯立式自定函數的整理
附錄D 第六章聯立式自定函數的整理
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