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研究生:陳玉奇
研究生(外文):CHEN,YU-CHI
論文名稱:非等向彈性體內含異質物之彈性波暫態散射問題之研究
論文名稱(外文):Study on the Transient Scattering of Elastic Waves from Inclusions in an Anisotropic Medium
指導教授:翁燈景翁燈景引用關係
指導教授(外文):D.C.Wong
學位類別:碩士
校院名稱:致遠管理學院
系所名稱:休閒設施規劃與管理學系碩士班
學門:民生學門
學類:運動休閒及休閒管理學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:中文
論文頁數:68
中文關鍵詞:柔性界面彈性波後散射場非等向彈性體
外文關鍵詞:compliant interfaceelastic waveback-scattered fieldanisotropic elastic soliddynamicafter
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本文探討二維無限域非等向彈性體內彈性波與異質物交互作用所產生之暫態散射情形。問題中非等向彈性體與異質物散射體之交界面考慮為具有柔性之界面層(Compliant Interface),並以連續之線性彈簧模式模擬柔性界面層之特性。兩個極端的物理散射情況可由此分析模式求得,其一為彈簧係數為無限大時可處理完全接合(Perfect Bonding)之問題,另一為彈簧係數為零時則可處理空洞散射體之問題。此外,當彈簧係數部份為零(但整個界面彈簧並不全為零)則可處理部份接觸問題(Partial Contact Problem)。本文所考慮的入射波為體波(P波及SV波)。
分析方法首先利用Fourier轉換將時域散射問題轉為頻率域散射問題,而後在頻率域內利用Betti-Rayleigh交互原理及二維無限域非等向動彈基本解推導出問題之邊界積分方程式(BIE)進而求得穩定狀態解,最後再利用快速Fourier反變換求得時間域之暫態解,以達到瞭解此物理問題的暫態散射狀態。
數值驗證將與非等向彈性體之散射問題作比較。數值結果將以頻率域及時間域兩方面之散射體邊界位移及後散射場(Back-scattered field)物理量表達,並就界面層之柔性程度、非等向材料性質及入射波之入射角度對這些物理量的影響進行討論。此些分析結果除了可應用於複合材料之超音波非破壞評估(NDE)方面之外,其分析模式亦可應用於機械業或半導體工業之薄膜力學動態問題之初步分析。
The two-dimensional ‘in-plane’ transient scattering problem of elastic waves with an isotropic inclusion in an infinite anisotropic elastic solid was analyzed. A compliant interface condition between the anisotropic elastic medium and its inclusion was considered and replaced by the distribution of linear springs in our analytical model. Limiting cases consisting of zero and infinite spring constants were then analyzed by the analytical model. Zero spring constant realized the case of cavity. Infinite spring constant was used to realize the case of perfect bonding. A partial contact problem was analyzed by parts of zero spring coefficients. Only quasi-P and quasi-SV waves were adapted as the incident plane waves.
The analytical method was implemented by Fourier transform such that problems in time domain were transformed into frequency domain. The boundary integral equations (BIE) were then to be made in frequency domain. The Betti-Rayleigh reciprocal theorem and a time-harmonic fundamental solution of an infinite anisotropic medium have made BIE ready in this research. When the boundary element method was implemented with appropriate boundary conditions, the BIE could subsequently be transformed into one set of linear simultaneous equations and solved numerically. Finally, the transient responses subjected to a step stress pulse were obtained by inversed Fourier transform after the steady state responses were reached in frequency domain.
The numerical calculations were validated by comparison with the isotropic cases. Numerical results were discussed in displacement fields on the boundary of a matrix side and the back-scattered fields in the anisotropic medium. The effects of the spring constants, material parameters, and the incident angles of elastic waves on physical quantities were also analyzed and discussed. The realization of effects of compliant interface on scattering problems can be implemented in NDE of composite materials. Results also indicated that it can be implemented in elementary analysis of membranes dynamic mechanics in mechanical industry as well as in semiconductor industry.
摘 要 I
Abstract II
誌 謝 IV
目 錄 IV
圖 目 錄 VI
第一章 緒 論 1
1-1 研究背景 1
1-2 文獻回顧 1
1-3 研究動機 3
1-4 研究內容及過程 3
第二章 基本方程式 5
2-1彈動問題之描述 5
2-2 入射波 7
2-3動態頻率域之基本解 10
2-3-1非等向彈性體 10
2-3-2等向性彈性體 13
2-4 頻率域之邊界積分方程式推導 14
第三章 具柔性介面之異質物散射問題分析 17
3-1頻率域下之邊界積分方程式 18
3-2問題之邊界條件 20
3-3數值方法 20
3-4 時間域之暫態解 24
第四章 數值結果與分析 25
4-1頻率域下之數值結果與討論 25
4-1-1等向性材料情況 25
4-1-2 正交性材料情況 26
4-1-3非等向材料情況 29
4-2時間域下之數值結果與討論 31
4-2-1等向性材料情況 31
4-2-2正交性材料情況 32
4-2-3非等向材料情況 32
第五章 結論 33
參 考 文 獻 34
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