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系統識別號 U0002-0203201115075100
中文論文名稱 雙層壓電複合材料受機電點載荷之暫態波傳問題
英文論文名稱 Transient Elastic Waves Propagating in a Two-Layered Piezoelectric Medium Subjected to the Mechanical and Electrical Concentrated Loadings
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 1
出版年 100
研究生中文姓名 黃國書
研究生英文姓名 Kuo-Shu Huang
學號 697430691
學位類別 碩士
語文別 中文
口試日期 2011-01-18
論文頁數 100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  反平面  機電點載荷  電位移 
英文關鍵字 Piezoelectric, Bimaterials  Anti-plane  Concentrated loadings  Electric displacement 
學科別分類 學科別應用科學航空太空
中文摘要 本文乃解析雙異質壓電複合層板承受反平面動力點載荷及平面電位移點載荷時之暫態波傳問題,此複合材料為由兩層不同厚度之壓電材料所構成的雙層複合條板。解析時,首先利用單邊與雙邊拉普拉斯積分轉換法求得兩次轉換域中的剪應力與電位移全場解,再利用Durbin單邊拉普拉斯數值逆轉換法以及延伸的雙邊拉普拉斯數值逆轉換法來求得暫態時域解。數值結果部分則針對不同觀察點位置、不同材料厚度比以及不同負載形式等情況作詳細計算與討論,並將本研究的特例與文獻上之雙層等厚板的靜力解作比較,以驗證本文數值結果的正確性。
英文摘要 In this study, transient elastic waves propagating in a two-layered piezoelectric medium subjected to anti-plane concentrated loading and in-plane electric displacement loading on the upper and lower free surfaces are investigated. The double-layer composite is constructed of two layers of piezoelectric materials with different thicknesses. The one-sided and the two-sided Laplace transforms are applied to obtain the shear stresses and the electric displacements in the transform domain. And then, the Durbin’s method for one-sided Laplace transform inversion and the extended Durbin’s method for two-sided Laplace transform inversion are used to carry out the numerical inversions. The numerical results for different field points, different ratios of thicknesses and different loading types 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.....................................................................................................IX
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............................................................................10
第二章 理論基礎............................................................................12
2.1 線性壓電材料控制方程式與本構方程式...............12
2.2 拉普拉斯轉換及逆轉換................................................14
2.3 Durbin方法.........................................................................15
2.4 簡單數值範例.....................................................................17
2.5 半無窮域壓電材料受反平面動力點載荷之暫態響 應..........................................................................................21
2.5.1 半無窮域壓電材料受反平面動力點載荷之解析....21
2.5.2 數值結果與比較........................................................26
第三章 雙異質壓電複合層板之暫態波傳解析...........................27
3.1 問題描述............................................................................27
3.2 雙異質壓電複合層板受反平面動力點載荷之解析......................................................................................29
3.3 雙異質壓電等厚層板受反平面動力點載荷之靜力解析.......................................................................................37
第四章 數值結果與討論............................................................40
4.1 數值計算說明.......................................................................40
4.2 數值結果與討論...................................................................41
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...................................................................50
參考文獻..........................................................................................52
附錄一 論文簡要版................................................................................93








圖 目 錄
圖2-1 於雙重數值拉普拉斯逆轉換的方法在不同 之比較.............................................................58
圖2-2 於雙重數值拉普拉斯逆轉換的方法在相同 ,不同 之比較.............................................59
圖 2-3 於雙重數值拉普拉斯逆轉換的方法在相同 ,不同 之比較.............................................60
圖 2-4 於雙重數值拉普拉斯逆轉換的方法在相同 ,不同 之比較................................................61
圖 2-5半無窮域壓電材料受反平面動力點載荷之結構示意圖..........62
圖2-6 半無窮域壓電材料受反平面動力點載荷利用雙重數值拉普拉 斯逆轉換與Cagniard-de Hoop method逆轉換於 觀察點位置所得到 數值解之比較............................................63
圖2-7 半無窮域壓電材料受反平面動力點載荷利用雙重數值拉普拉斯逆轉換與Cagniard-de Hoop method逆轉換於 觀察點位置所得到 數值解之比較............................................64
圖2-8 半無窮域壓電材料受反平面動力點載荷利用雙重數值拉普拉斯逆轉換與Cagniard-de Hoop method逆轉換於 觀察點位置所得到 數值解之比較............................................65
圖3-1雙異質壓電複合層板受反平面動力點載荷與平面電位 移點載荷負載之圖形...........................................................66
圖 3-2 雙異質壓電等厚層板受載荷作用之圖形.......................67
圖3-3 雙異質壓電等厚層板的兩負載所產生的應力場疊加之示意圖............................................................................68
圖4-1觀察點在(0,0)位置的剪應力 之暫態數值解與靜力解比較................................................................................................69
圖4-2 觀察點在 位置的剪應力 之暫態數值解與靜力解 比較...............………………………...…………………………70
圖4-3 觀察點在 位置的剪應力 之暫態數值解與靜力 解比較.................………………………………...……...………71
圖4-4 觀察點在 位置的剪應力 之暫態數值解與靜力解 比較.................…………………………………......………....…72
圖4-5 觀察點在 位置的剪應力 之暫態數值解與靜力解比較.................……………………………………...…...…....…....73
圖4-6觀察點在(0,0)位置於長時間的剪應力 之暫態數值圖.........74
圖4-7觀察點在(0,0)位置的剪應力 之暫態數值圖............................75
圖4-8觀察點在 之不同位置的剪應力 之暫態數值圖....76


圖 4-9 觀察點在 之不同位置的剪應力 之暫態數值圖..........77
圖 4-10觀察點在 之不同位置的剪應力 之暫態數值圖..78
圖 4-11觀察點在 之不同位置僅施加電位移負載的剪應力 之暫態數值圖..........................................................………....…....79
圖4-12 觀察點在 之不同位置僅施加電位移負載的剪應力 之暫態數值圖.............………………………........………....…....80
圖4-13觀察點在 之不同位置僅施加電位移負載的剪應力 之暫態數值圖..................................................................................81
圖 4-14 觀察點在(0,0)位置雙層材料之不同厚度比的剪應力 之暫態數值圖.................…………………………………....….........82
圖 4-15 觀察點在(0,0)位置雙層材料之不同厚度比的剪應力 之暫態數值圖...........................………………………………....…....83
圖4-16觀察點在(0,0)位置雙層材料之不同厚度比僅施加電位移負載的剪應力 之暫態數值圖......…………….....………....…....84
圖 4-17 觀察點在(0,0)位置施加不同電位移負載大小的剪應力 之暫態數值圖.................……………….....………………....…....85
圖 4-18 觀察點在 之不同位置的電位移 之暫態數值圖.......
....................................................................................................................86
圖 4-19 觀察點在 之不同位置的電位移 之暫態數值圖.............
....................................................................................................................87
圖 4-20 觀察點在 之不同位置的電位移 之暫態數值圖....
....................................................................................................................88
圖 4-21 觀察點在(0,0)位置雙層材料之不同厚度比的電位移 之暫 態數值圖.................……………….....………………....…........89
圖4-22 觀察點在(0,0)位置施加不同機械應力大小的電位移 之暫態數值圖.................……………….....………………....…........90
圖4-23 觀察點在 位置雙層材料之不同厚度比施加機械應力產生頭前波效應的 之暫態數值圖...........................…....91
表 目 錄
表4-1 壓電常數表……………………………………………………..92


參考文獻 Cagniard, L., (1939) Reflexion et Refraction des Ondes Seismiques Progressives, Cauthuers–Villars,Paris;Translated into English and revised by Flinn, E. A. and Dix, C. H., (1962) Reflection and refraction of Progressive Seismic Waves, McGraw Hill, New York.

Crump K. S., (1976) “Numerical inversion of the Laplace transforms using a Fourier series approximation,” Journal of the Association for Computing Machinery 23, 89–96.

Choi, H. J. and Thangjithan, S., (1991) “Micro– and macromechanical stress and failure analysis of laminated composites,” Composites Science and Technology 14, 289–305.

de Hoop, A. T., (1958) Representation theorems for the displaycement in an elastic solid and their application to elastodynamic diffraction theory, Doctoral dissertation, Technische hoegschool, Delft.

Dubner, H. and Abate, J., (1968) “Numerical inversion of Laplace transforms by relating them to the finite Fourier cosine transform,” Journal of the Association for Computing Machinery 15, 115–123.

Durbin, F., (1974) “Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate’s method,” The Computer Journal 17, 371–376.

Fan, J. L. and Ye, J. Q., (1990) “An exact soluteion for the statics and dynamics of laminted thick plate with orthotropic layers,” International Journal of Solids and Structures 26, 655–662.

Haskell, N., (1953) “The dispersion of surface waves on multilayered media,” Bulletin of the Seismological Society of America 43, 17–34.

Honig, G. and Hirdes, U., (1984) “A method for the numerical inversion of Laplace transforms,” Journal of Computational and Applied Mathematics 10, 113–132.

Jiang, L. Z. and Lee, J. S., (1996) “Exact electroelastic analysis of piezoelectric laminate via state space approach,” International Journal of Solids and Structures 33, 977–990.

Jiang, C. P. and Cheung, Y. K., (2001) “An exact eolution for the three-phase piezoelectric cylinder model under antiplane shear and its application to piezoelectric composites,” Intertional Journal Solids and Structures 38, 4777–4796.

Kennett B. L. N. and Kerry, N. J., (1979) “Seismic waves in a stratified half space,” Geophysical Journal. Royal Astronomical Society 44, 557–583.

Kitahara, N., Nagahara, D. and Yano, H., (1988) “Numerical inversion of Laplace transform and its application,” Journal of the Franklin Institute 325, 221–233.

Kwok, Y. K. and Barthez, D., (1989) “An algorithm for the numerical inversion of Laplace transforms,” Inverse Problems 5, 1089–1095.

Krommer, M., (2003) “Piezoelectric vibrations of composite Reissner-Mindlin-type plates,” Journal of Sound and Vibration 263, 871–891.

Lin, W. and Keer, L. M., (1989) “Analysis of a vertical crack in a multilayered medium,”ASME Journal of Engineering for Industry 56, 63–69.

Lee, P. C. Y. and Wang, J., (1996) “Thickness-shear and flexural vibrations of contoured crystal strip resonators,” Journal of Applied Physics 79, 3403–3410.

Liu, J. X. Du, S. Y. and Wang, B., (1999) “A screw dislocateion with a piezoelectric biomaterial interface,” Mechanics Research Communications 26, 415–420.

Lin, R. L. and Ma, C. C., (2000) “Antiplane deformations for anisotropic multilayered media by using the coordinate transform method,”ASME Journal of Applied Mechanics 67, 597–605.

Li, S., (2000) “Transient wave propagation in a transversely isotropic piezoelectric half space,”Zeitschrift fur Angewandte Mathematik und Physik 51, 236–266.

Liu, X. Wang, Q. and Quek, S. T., (2002) “Analytical soluteion for free vibration of piezoelectric coupled moderately thick circular plates,” Journal of Sound and Vibration 245, 133–150.

Li, X. F. and Lee, K. Y., (2004) “Dynamic behavior of a piezoelectric ceramic layer with two surface cracks ,” International Journal of Solids and Structures 41, 3193–3209.

Li, X. F. and Yang, J., (2005) “Electromagnetoelastic behavior induced by a crack under antiplane mechanical and inplane electric impacts,” International Journal of Fracture 132, 49-64.

Loeber, J. F. and Sih, G. C., (1968) “Diffraction of antiplane shear waves by a finite crack,” The Journal of the Acoustical Society of America 44, 90–98.

Li, X. F. and Lee, K.Y., (2006) “Transient response of a semi-infinite piezoelectric layer with a surface permeable crack ,” Zeitschrift fur Angewandte Mathematik und Physik 57, 636–651.

Miller, M. K. and Guy, W. T.,(1966) “Numerical inversion of the Laplace transform by use of Jacobi polynomials,” SIAM Journal on Numerical Analysis 3, 624–635.

Muller, G., (1968a) “Theoretical seismograms for some types of point-source in layered media:Part Ⅰ:Theory,” Z. Geophys. 34, 15–35.
Muller, G., (1968b) “Theoretical seismograms for some types of point-source in layered media:Part Ⅱ:Numerical calculations,” Z. Geophys. 34, 247–371.

Muller, G., (1969) “Theoretical seismograms for some types of point-source in layered media:Part Ⅲ:Single force and dipole source of arbitrary orientation,” Z. Geophys. 35, 347–371.

Ma, C. C. and Huang, K. C., (1995) “Analytical transient analysis of layered composite medium subjected to dynamic in-plane impact loadings,” International Jiurnal Solids and Structures 33, 4511–4529.

Ma, C. C. and Huang, K. C., (1996) “Exact transient solutions of buried dynamic point forces for elastic bi-materials,” International Jiurnal Solids and Structures 33, 4223–4238.

Meguid, S. A. and Deng, W., (1999) “Analysis if a screw dislocateion inside an elliptical inhomogeneity in piezoelectric solids,” International Journal of Solids and Structures 36, 1449–1469.

Ma, C. C. and Lee, G. S., (2000) “Transient elastic waves propagating in a multi-layered medium subjected to in-plane dynamic loadings. . Theory,”Proceedings of the Royal Society of London 456, 1355–1374.

Ma, C. C. and Lee, G. S., (2000) “Transient elastic waves propagating in a multi-layered medium subjected to in-plane dynamic loadings. . Numerical calculation and experimental measurement,” Proceedings of the Royal Society of London 456, 1375–1396.

Meguid, S. A. and Chen, Z. T., (2001) “Transient response of a finite piezoelectric strip containing coplanar insulating cracks under electromechanical impact,” Mechanics of Materials 33, 85–96.



Ma, C. C. Chen, X. H., and Ing, Y. S., (2007) “Theoretical transient analysis and wave propagation of piezoelectric bi-materials,” International Journal of Solids and Structures 44, 7110–7142.

Pak, Y. E., (1990) “Force on a piezoelectric dislocation,” Journal of Applied Mechanics 57, 863–869.

Schmittroth, L. A., (1960) “Numerical inversion of Laplace transforms,” Communications of the ACM 3, 171–173.

Spencer, T. W., (1960) “The method of generalized reflection and transmission coefficients,”Geophysics. 25, 625–641.

Small, J. C. and Booker, J. R., (1984) “Finite layer analysis of layered elastic materials using a flexibility approach. part 1-strip loadings,” International Journal for Numerical Methods in Engineering 20, 1025–1037.

Thomson, W. T., (1950) “Transmission of elastic waves through a stratified solid medium,” Journal of Applied Physics 21, 89–93.

Tiersten, H. F., (1969) “Linear piezoelectric plate viberaction,” Plenum Press, New York.

Therapos, C. P. and Diamessis, J. E., (1982) “Numerical inversion of a class of Laplace transforms,” Electronics Letters 18, 620–622.

Tzou, H. S. and Zhong, J. P., (1994) “A linear theory of piezoelectric shell vibrations,” Journal of Sound and Vibration 175, 77–88.

Wang, B. L., Han, J. C. and Du, S. Y., (2000) “Electroelastic fracture dynamics for multilayered piezoelectric materials under dynamic anti-plane shearing,” International Journal of Solids and Structures, 37, 5219–5231.



Wang, X. and Yu, S., (2000) “Transient response of a crack in a piezoelectric strip subjected to the mechanical and electrical impacts,” International Journal of Solids and Structures 37, 5795–5808.

Zakian V. and Coleman R., (1971) “Numerical inversion of rational Laplace transforms,” Electronics Letters 7, 777–778.

Zhao, X. and Meguid, S. A., (2002) “The interface crack problem of bonded piezoelectric and elastic half-space under transient electromechanical loads ,”Journal of Applied Mechanics, Transactions of the ASME 69, 244–253.

王思元 (2003),壓電材料層域角域及圓形域之力學與電學全場解析,國立台灣大學機械工程學研究所碩士論文。

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。
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