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中文論文名稱 含界面裂紋之雙層壓電複合層板受平面動力負載之暫態響應
英文論文名稱 Transient response of an interface crack between two piezoelectric layers under mechanical impacts
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 99
學期 2
出版年 100
研究生中文姓名 林子翔
研究生英文姓名 Tzu-Hsiang Lin
學號 698430088
學位類別 碩士
語文別 中文
口試日期 2011-07-20
論文頁數 67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 壓電  複合層板  界面裂紋  應力強度因子  平面  動力破壞  暫態 
英文關鍵字 piezoelectric  Bimaterials  Interface crack  Stress intensity factor  In-plane  Dynamic fracture  Transient 
學科別分類 學科別應用科學航空太空
中文摘要 本文研究含界面裂紋之雙層壓電複合層板受平面動力負載之暫態響應,解析一含有限長可滲透性裂紋之雙層複合壓電材料,於裂紋面承受平面正向應力與平面剪應力動力負載之暫態問題。本文使用拉普拉斯轉換、傅立葉轉換、奇異積分方程、Jacobi 多項式重新解析Gu et al.(2002)已求解過的問題。本文求得的應力強度因子解析解與Gu et al.(2002)所獲得的結果並不相同,且數值計算結果有很大的差異。本文計算時域中之應力強度因子,乃採用Durbin 之數值拉普拉斯逆轉換法,所獲得的暫態圖形比Gu et al. (2002)的結果更能看出各個反射波與繞射波的到達現象。
英文摘要 In this study, transient response of an interface crack between two piezoelectric layers is investigated. The composite is subjected to uniformly in-plane mechanical impacts under permeable boundary conditions. The integral transform, Cauchy singular integral equation methods, and Jacobi polynomials expansions are applied to obtain the solutions in the Laplace transform domain. Durbin’s method is used to carry out the numerical inversion of Laplace transform. The accuracy of numerical results is examined and the applicable numerical parameters are suggested by the
experience of calculation. Finally, the numerical results are evaluated and discussed in detail.
論文目次 中文摘要 ………………………………………………………………I
英文摘要………………………………………………………………II
目錄……………………………………………………………………III
圖目錄……………………………………………………………………V
表目錄…………………………………………………………………VI
第一章 緒論…………………………………………………………1
1.1 研究動機……………………………………………………1
1.2 文獻回顧……………………………………………………4
1.3 內容簡介……………………………………………………7
第二章 理論基礎………………………………………………8
2.1 壓電控制方程式及本構方程式……………………………8
2.2 拉普拉斯轉換及逆轉換……………………………………10
2.3 傅立葉轉換及逆轉換……………………………………10
2.4 奇異積分方程 (Singular Integral Equation) ………………10
2.5 Jacobi 多項式………………………………………………11
2.6 Durbin 方法…………………………………………………12
第三章 含界面裂紋之雙異質壓電複合層板受平面動力負載之
暫態響應……………………………………………………14
3.1 問題描述……………………………………………………14
3.2 含可滲透性界面裂紋之雙異質壓電層板承受平面動力
負載之暫態響應解析……………………………………16
第四章 數值結果與討論……………………………………………42
4.1 數值運算分析……………………………………………42
4.2 數值結果與比較……………………………………………45
第五章 結論與成果…………………………………………………48
5.1 本文結論……………………………………………………48
5.2 本文成果……………………………………………………49
5.3 尚待研究的方向……………………………………………49
參考文獻………………………………………………………………51
附錄一論文簡易版 ……………………………………………………60

圖 目 錄
圖3-1 含界面裂紋之雙異質壓電複合層板之圖形…………………54
圖4-1 應力強度因子於不同加總項數上限之比較…………………55
圖4-2 應力強度因子於不同層板厚度之比較………………………56
圖4-3 應力強度因子於厚層板時不同加總項數上限之比較………57
圖4-4 核函數 積分取至不同上限之比較 ………………58

表 目 錄
表4-1 壓電材料常數表………………………………………………59
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Durbin, F., “Numerical inversion of Laplace transforms: an efficient improvement to Duber and Abate’s method”, The Computer Journal, Vol. 17, pp. 371–376, 1974.

Erdogan, F., “Approximate solutions of systems of singular integral equations”, SIAM Journal on Applied Mathematics, Vol. 17, No. 6, pp. 1041-1059, Nov., 1969.

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Gupta, V., Argon, A.S., Suo, Z., “Crack deflection at an interface between two orthotropic materials”, Journal of Applied Mathematics, Vol. 59, pp. 79-87, 1992.

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Lee, K.Y., Takahashi, H., “Fracture and Strength’90”, Trans Tech Publications, ISBN. 0-87849-618-1, 1991.

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Qin, Q.H., Zhang, X., “Crack deflection at an interface between dissimilar piezoelectric materials”, International Journal of Fracture, Vol. 102, pp. 355-370, 2000.

Rice, J.R., “Elastic fracture mechanics concepts for interfacial cracks”, Journal of Applied Mechanics, Vol. 55, pp. 98-103, 1988.

Shen, S.P., Kuang, Z.B., “Wave scattering from an interface crack in laminated anisotropic media”, Mechanics Research Communications, Vol. 25, No. 5, pp. 509-517, 1998.

Shen, S.P., Kuang, Z.B., Hu, S.L., “Interface crack problems of a laminated piezoelectric plate”, Journal of Mechanics and Solids, Vol. 18, pp. 219-238, 1999.

Suo, Z., Kuo, C.M., Barnett, D.M., Willis, J.R., “Fracture mechanics for piezoelectric ceramics”, Journal of the Mechanics and Physics of Solids, Vol. 40, No. 4, pp. 739-765, 1992.

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materials”, International Journal of Fracture, Vol. 98, pp. 15-35, 1999.

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Zhao, X., “An efficient approach for the numerical inversion of Laplace transform and its application in dynamic fracture analysis of a piezoelectric laminate”, International Journal of Solids and Structures,
Vol. 41, pp. 3653-3674, 2004.

廖雪吩 (2007),應用數值拉普拉斯逆轉換法於壓電材料動力破壞之研究,淡江大學航空太空工程學系碩士班碩士論文。

許吉勝 (2008),含有限長裂紋之彈壓電複合層板動力破壞分析,淡江大學航空太空工程學系碩士班碩士論文。

余智瑋 (2009),含有限長裂紋之雙異質壓電複合層板動力破壞分析,淡江大學航空太空工程學系碩士班碩士論文。
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