臺灣博碩士論文加值系統

Pride (1994) 理論藉由融合了Biot (1956) 對於孔隙彈性材料的理論，馬克斯威爾方程式，和通量/力傳輸方程式而來。本論文係基於此理論，並將Pao(1978) 對於彈性介質的推演，和Yeh et al. (2004) 對於彈性多孔隙介質的推導，而建立孔隙導電彈性介質的轉換矩陣。在推導的過程中，將耦合的運動方程式解耦為兩個部份：一部分描述膨脹(dilatational)(縱(longitudinal))波，另一部份描述轉動(rotational)(橫(transverse))波。上述的縱波包括Biot (1962) 理論的快波和慢波，而橫波包括力學剪力波和電磁波。在論文中，也利用Wronskian公式，證明解析形式的基函數具有正交的關係。為了顯示用轉換矩陣法解析震電效應的結果，文中建立一例：在孔隙導電彈性介質中，埋置一異質圓球狀導電孔隙彈性介質，分析當它承受平面入射壓力波時，波的散射現象。

On the basis of Pride’s theory (1994), which couples Biot’s theory for poroelastic medium (1956) and Maxwell equations via flux/force transport equations, we extend Pao (1978) and Yeh et al. (2004) approaches for elastic medium and poroelastic medium, respectively, to develop a transition matrix for electroporoelastic medium. During the process of derivation, we decouple our motion equations into two parts; one is dilatational (longitudinal) wave and the other is rotational (transverse) wave. The above mentioned longitudinal wave includes the fast wave and slow wave components. Regarding with transverse wave, it includes shear wave and electromagnetic wave. In this thesis, we also utilize the Wronskian formula to prove that our analytical base functions have orthogonality. To illustrate the application, we consider a simple case of the scattering problem of a spherical electroporoelastic inclusion, embedded within the surrounding electroporoelastic medium subjected to an incident plane compressional wave.

口試委員會審定書…………………………...………...………… i
誌謝………………………………………..……………..………. ii
中文摘要……………………………………..…………….….… iii
英文摘要………………………………………………..…….…. iv
第一章 緒論
1.1 前言………..………….……………….………………………1
1.2 震電效應研究發展………………….………………………….2
1.2.1 震電效應的觀測和實驗…………….…………………………2
1.2.2 震電效應的理論研究及數值分析………………….…………3
1.3 本文內容……………………………………….……………….4
第二章 孔隙導電彈性介質中聲電耦合波御制方程式
2.1 孔隙和顆粒御制方程式………………………….…………….7
2.1.1 電雙層模型…………………………………….………………7
2.1.2 電磁方程式…………………………………….………………7
2.1.3 力學方程式………………………………….…….……..…12
2.2 平均御制方程式…………………………….…….….….….12
2.2.1 平均電磁方程式…………………………….…….….…….13
2.2.2 平均力學方程式……………………………………..……..17
2.3 邊界值問題……………………………………….….……...20
2.3.1 孔隙導電彈性介質中的電場和離子數密度偏差量….…...20
2.3.2 孔隙中的流場………………………………….…….……..24
2.4 轉換係數………………………………………..……….….27
2.4.1 導體電流 和 ………………………………………………..28
2.4.2 流動電流 …………………………………………….……..29
2.4.3 相對流速 …………………………………….……….…...32
2.4.4 最後係數……………………………………….…….……..34
第三章 T-矩陣法運用於無限域中孔隙導電彈性介質之震電波之散射問題
3.1 基函數和正交條件…………………………………………...36
3.1.1 御制方程式…………………………………………………..36
3.1.2 運動方程式的解耦………………………………….….…..37
3.1.3 球座標系統下的基函數……………………….…….……..42
3.1.4 正交條件……………………………………….….………..46
3.2 孔隙導電彈性介質的T-矩陣公式…………….….…….…..49
3.2.1 入射、折射和散射波之級數展開……………….…….…..49
3.2.2 針對異質球型孔隙導電彈性介質埋置物的T-矩陣公式.….50
3.3 數值結果…………...…………………………………..……53
3.4 本章結語………………………………………….….……...55
第四章 結論與未來展望
4.1 結論……………………………………….…….………...56
4.2 未來研究展望………………………..….…………………57
4.2.1 向量基函數的傅氏譜表述式……………………………....58
4.2.2 自由表面反射之反射波推導………………………………..69
參考文獻…………………………………….…………….………….73
附錄A 依據Lamé勢能改寫………………..…………………………92
附錄B 孔隙導電彈性介質中耦合縱、橫波的解耦過程……………96
附錄C 孔隙導電彈性介質中埋置孔隙導電彈性材質球所構成Q矩陣之子元素及相關正交條件證明………..……………….…….…..100
附錄D 數值模擬部分之宏觀轉換係數………………….………..109
附錄E 符號表………………………………………………….…..112

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