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研究生:徐裕旼
研究生(外文):Yu-Min Hsu
論文名稱:多個圓弧山峰承受平面水平剪力波的反應
論文名稱(外文):Response of Multiple Circular-Arc Hill subjected to Plane SH-Waves
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:碩士
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:2004
畢業學年度:92
語文別:中文
論文頁數:232
中文關鍵詞:平面水平剪力波多個圓弧山峰散射領域媒親法
外文關鍵詞:plane SH-wavesmultiple circular-arc hillscatteringfield-matching method
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本文以領域媒親法(Field-Matching Method)解析多個圓弧山峰承受平面水平剪力波作用後的地表位移反應。首先在求解過程中,將整個求解領域分割成多個子領域,並將各子領域以滿足Helmholtz方程之波函數展開來表示,然後在各相鄰子領域的交界線上利用座標轉換關係式將各領域座標轉換成局部座標系統後,再配合選點法即可建構出聯立方程組來求得各子領域中的未定係數。文中分別針對多個半圓弧及淺圓弧山峰來探討入射波不同無因次頻率、入射角度與山峰之寬高比對地表位移反應的影響。本文所有數值計算例之結果在與邊界元素法所得結果比對後,發現兩者近乎重合,驗證了本文方法的正確性及可靠性。根據本文數值計算例結果得知,在多個半圓弧山峰地形,當入射波為正向入射且半圓弧山峰寬度為入射波波長的整數倍時,在山峰內會有波集中而造成地表位移幅值升高,會比無山峰存在時的位移幅值要高兩倍多。
The thesis investigates the response of multiple circular-arc hills subjected to plane SH-waves by using the field-matching method. In the process of analysis, the entire domain is divided into some sub-domains and the displacement functions are in terms of wave functions for each sub-domain. The wave functions satisfy the Helmholtz equation. At the interface between neighboring sub-domains, the coordinate systems in each sub-domain are then converted into local coordinate systems by utilizing coordinate transformation formulas. By applying the collocation method to constitute simultaneous equations, the unknown coefficients in each sub-domain can be determined. The computational solutions are presented to illustrate the effects of various dimensionless frequencies, angle of wave incidence, and height-to-width ratio of hills on the surface ground motions. Furthermore, the validity of the proposed method is verified by solutions for the boundary element approach. It is also shown that both of them agree fairly well with each other. In the normal incident cases, as the ratio of the width of semi-circular hill to the incident wave length is an integer, the surface ground amplification could be two times more than that for the surface without any hill. This is due to the incident, reflected, and scattered waves concentrated into the hill.
中文摘要 i


英文摘要 ii


目錄 iii


圖目錄 v


第一章 緒論 1


1 - 1 前言 1

1 - 2 研究動機 3

1 - 3 文獻回顧 3

1 - 4 研究方法 4

1 - 5 內容架構 5

第二章 理論分析 7

2 - 1 緒論 7

2 - 2 彈性力學問題的基礎理論 10

2 - 3 控制方程的建立 13

第三章 多個半圓弧山峰的散射反應 18

3 - 1 問題描述與基本方程式 18

3 - 1 - 1 問題的描述 18

3 - 1 - 2 基本方程式 18

3 - 2 分析方法及步驟 20

3 - 2 - 1 單一半圓弧山峰數值模型 20

3 - 2 - 2 兩個相同半圓弧山峰數值模型 24

3 - 2 - 3 多個半圓弧山峰數值模型 32

3 - 3 數值計算例及討論 33

3 - 3 - 1 單一半圓弧山峰 33

3 - 3 - 2 兩個半圓弧山峰 34

3 - 3 - 3 三個半圓弧山峰 36


第四章 多個淺圓弧山峰的散射反應 103

4 - 1 問題描述與基本方程式 103

4 - 1 - 1 問題的描述 103

4 - 1 - 2 基本方程式 103

4 - 2 分析方法及步驟 105

4 - 2 - 1 單一淺圓弧山峰數值模型 105

4 - 2 - 2 兩個相同淺圓弧山峰數值模型 110

4 - 2 - 3 多個淺圓弧山峰數值模型 119

4 - 3 數值計算例及討論 120

4 - 3 - 1 單一淺圓弧山峰 120

4 - 3 - 2 兩個淺圓弧山峰 121

4 - 3 - 3 三個淺圓弧山峰 123


第五章 結論 230


參考文獻 231
Graff, K. F. (1975) Wave motion in elastic solids, Ohio State University.

Achenbach, J. D. (1984) Wave Propagation in elastic solids, North-Holland.

Fang, Y. (1995) "Series solution for scattering of plane SH-waves by multiple shallow circular-arc canyons," Applied Mathematics and Mechanics, Vol. 16, No. 7, pp. 657-666.

Hayir, A., M. I. Todorovska, and M. D. Trifunac (2001) "Antiplane response of a dike with flexible soil-structure interface to incident SH-waves," Soil Dynamics and Earthquake Engineering, Vol. 21, pp. 603-613.

Lee, V. W., S. Chen, and I. R. Hsu (1999) "Antiplane diffraction from canyon above subsurface unlined tunnel," Jornal of Engineering Mechanics, Vol. 125, pp. 668-675.

Sills, L. B. (1978) "Scattering of horizontally-ploarized shear waves by surface irregularities," The Geophysical Journal of the Royal Astronomical Society, Vol. 54, pp. 319-348.

Trifunac, M. D. (1973) "Scattering of plane SH-waves by a semi-cylindrical canyon," Earthquake Engineering And Structural Dynamics, Vol. 1, pp. 267-281.

Yuan, X. and F. Men (1992) "Scattering of plane SH-waves by a semi-cylindrical hill," Earthquake Engineering And Structural Dynamics, Vol. 21, pp. 1091-1098.

Yuan, X. and Z. Liao (1994) "Scattering of plane SH-waves by a cylindrical canyon of circular-arc cross-section," Soil Dynamics and Earthquake Engineering, Vol. 13, pp. 407-412.

Yuan, X. and Z. Liao (1996) "Surface motion of a cylindrical hill of circular-arc cross-section for incident plane SH-waves," Soil Dynamics and Earthquake Engineering, Vol. 15, pp. 189-199.

梁昆淼 (1978) 數學物理方法,高等教育。

吳家龍 (1996) 彈性力學,上海同濟大學。

孫家樂、曹淑芳、楊琪瑜 (2000) 偏微分方程—原理及題解,中央圖書出版社。

蔡宜璋 (1998) 半無限域中散射體承受傾斜入射波引起之散射現象,國立台灣大學土木工程學研究所博士論文。

徐文信 (2002) 震波在含夾物半平面之散射行為,國立台灣大學土木工程學研究所博士論文。
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