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系統識別號 U0002-0607200912275700
中文論文名稱 含界層裂紋之雙異質壓電材料在半雙曲線近似下之暫態解析
英文論文名稱 Transient analysis of an interface crack in piezoelectric bimaterials due to Quasi-hyperbolic Approximation
校院名稱 淡江大學
系所名稱(中) 航空太空工程學系碩士班
系所名稱(英) Department of Aerospace Engineering
學年度 97
學期 2
出版年 98
研究生中文姓名 陳彥廷
研究生英文姓名 Yen-Ting Chen
學號 696430221
學位類別 碩士
語文別 中文
口試日期 2009-07-01
論文頁數 147頁
口試委員 指導教授-應宜雄
委員-馬劍清
委員-劉昭華
中文關鍵字 暫態  界面裂紋  應力強度因子  壓電材料 
英文關鍵字 piezoelectric material  interface crack  stress intensity factor 
學科別分類 學科別應用科學航空太空
中文摘要 本文研究內含電極邊界之界面裂紋的壓電複合材料動力破壞問題,解析一含半無限長界面裂紋之六角雙異質壓電材料複合層板,於裂紋面上施加反平面動力點載荷在有限光速影響下之暫態效應,本文利用積分轉換法與Wiener-Hopf技巧推導壓電材料於拉普拉斯轉換域中之基本解,接著利用疊加的技巧求得一次拉普拉斯轉換域中之解,最後在使用Cagniard-de Hoop Method來做拉普拉斯逆轉換得到時域中的全場暫態解析解,並求出應力強度因子與電位移強度因子等解析解。最後,將針對應力與電位移之暫態解作數值計算與討論。
英文摘要 In this study, the transient response of a semi-infinite interface crack due to Quasi-hyperbolic approximation between two dissimilar piezoelectric materials with the electrode boundary condition is investigated. The useful fundamental solutions are derived and the solutions can be determined by superposition of the fundamental solutions in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in Laplace transform domain) on the interface crack faces. The Cagniard-de Hoop method of Laplace inversion is used to obtain the transient solution in time domain. Exact transient Full-Field solution and exact transient solution of intensity factors to the problem with concentrated loads are derived. Finally, numerical results are evaluated and discussed in detail.
論文目次 目錄
目錄......................................................I
圖表目錄................................................III
附錄.....................................................VI
第一章 緒論
1.1研究動機顧...........................................1
1.2文獻回顧.............................................3
1.3內容簡介.............................................7
第二章 理論基礎
2.1麥斯威爾方程式.......................................8
2.2線性壓電控制與本構方程式............................10
2.3拉普拉斯轉換與Cagniard-de Hoop method...............18
2.4含靜止裂紋之雙異質壓電材料在有限光速影響下受反平面應力
型負載基本解........................................19
2.5存在MT表面波N(λ)有實根之理論分析....................30
2.6無MT表面波N(λ)無實根之理論分析......................38
第三章 界面裂紋受反平面動力點載荷之暫態解析
3.1問題描述.............................................46
3.2存在MT表面波之解析...................................47
3.3無MT表面波之解析.....................................72
3.4結果驗證.............................................89
第四章 數值計算與討論.....................................96
第五章 成果與討論........................................102
5.1本文結論............................................102
5.2本文成果............................................103
5.3尚待研究方向........................................103
參考文獻.................................................105
圖表目錄
圖3-1 介面裂紋之問題描述.................................109
圖3-2 逆轉換路徑圖有剪力頭前波..........................110
圖3-3 逆轉換路徑圖無剪力頭前波..........................111
圖3-4 逆轉換路徑圖有剪力頭前波..........................112
圖3-5 逆轉換路徑圖無剪力頭前波..........................113
圖3-6a 之雙異質壓電材料裂紋面施加動力點載荷波前.........114
圖3-6b 之雙異質壓電材料裂紋面施加動力點載荷波前放圖.....115
圖3-7 時,有MT表面波圍線積分路徑圖......................116
圖3-8 時,有MT表面波圍線積分路徑圖......................117
圖3-9 時,無MT表面波圍線積分路徑圖......................118
圖3-10 時無MT表面波圍線積分路徑圖.......................119
表4.1 壓電材料常數表.....................................120
表4.2 有限光速影響下與光速趨近無限大之應力強度因子數值比較
(ZnO-PZT4).........................................121
表4.3 有限光速影響下與光速趨近無限大之電位移強度因子
數值比較(ZnO-PZT4).................................122
圖4-1a 積分路徑圖.......................................123
圖4-1b 積分路徑圖.......................................124
圖4-2數值積分示意圖......................................125
圖4-3 (4.1)式圍線積分路徑圖..............................126
圖4-4 受應力負載含界面裂紋在有限光速影響下之應力強度因子
(ZnO-PZT4) ........................................127
圖4-5 受應力負載含界面裂紋在有限光速影響下之電位移強度因子
(ZnO-PZT4) ........................................128
圖4-6 受應力負載含界面裂紋在有限光速影響下之應力強度因子
(PZT4-CdS) ........................................129
圖4-7 受應力負載含界面裂紋在有限光速影響下之應力強度因子
(虛擬材料-PZT4) ..................................130
圖4-8 受應力負載含界面裂紋在有限光速影響下之電位移強因子
(虛擬材料-PZT4)....................................131
圖4-9 受應力負載含界面裂紋在光速趨近無限大之應力強度因子
(ZnO-PZT4) ........................................132
圖4-10 受應力負載含界面裂紋在光速趨近無限大之電位移強度因子
(ZnO-PZT4) .......................................133
圖4-11 受應力負載含界面裂紋在光速趨近無限大之應力強度因子
(虛擬材料-PZT4) ..................................134
圖4-12 受應力負載含界面裂紋在光速趨近無限大之電位移強度因子
(虛擬材料-PZT4) ..................................135
圖4-13 受應力負載含界面裂紋在有限光速影響下與光速趨近無限大
之應力強度因子比較 (虛擬材料-PZT4)................136
圖4-14 受應力負載含界面裂紋在有限光速影響下與光速趨近無限大
之電位移強度因子比較 (虛擬材料-PZT4)..............137
圖4-15 受應力負載含界面裂紋單一壓電材料在有限光速影響下之應
力強度因子(PZT4)..................................138
圖4-16 受應力負載含界面裂紋單一壓電材料在有限光速影響下之電
位移強度因子(PZT4)................................139
附錄
附錄一...................................................140
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王茂榮, (2003),含擴展裂紋之壓電材料動力破壞解析,淡江大學航空太空工程學所碩士論文。

蔡忠翰, (2005),含界層裂紋之彈壓電複合材料之動力破壞分析,淡江大學航空太空工程學所碩士論文。

黃俊元, (2006),含界面裂紋之雙異質壓電材料暫態解析,淡江大學航空太空工程學所碩士論文。

謝友誌, (2007),半雙曲線近似對含裂紋之壓電材料動態特性影響之研究,淡江大學航空太空工程學所碩士論文。

陳冠志, (2008),含界層裂紋之雙層壓電材料受反平面動力點載荷之暫態效應,淡江大學航空太空工程學所碩士論文。
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