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系統識別號 U0002-0708201212223800
中文論文名稱 雙異質壓電複合層板內受單一點載荷之暫態波傳分析
英文論文名稱 Transient Analysis of a Two-Layered Piezoelectric Medium Subjected to Dynamic Mechanical and Electrical Point Loading
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 100
學期 2
出版年 101
研究生中文姓名 黃健彰
研究生英文姓名 Chien-Chang Huang
學號 698430518
學位類別 碩士
語文別 中文
口試日期 2012-07-10
論文頁數 76頁
口試委員 指導教授-應宜雄
委員-馬劍清
委員-黃育熙
中文關鍵字 壓電  複合層板  暫態  波傳  電位移 
英文關鍵字 Piezoelectric  Bimaterials  Transient  Wave propagation  Electric displacement 
學科別分類 學科別應用科學航空太空
中文摘要 本文解析雙異質壓電複合層板承受單一動力機械點載荷及電位移點載荷之暫態波傳問題,此結構是由兩層不同厚度之壓電材料構成的雙層複合層板,並在上層材料內施予動力點載荷。解析時,首先利用單邊及雙邊拉普拉斯轉換求得兩次轉換域中的剪應力及電位移之全場解,再利用Durbin單邊拉普拉斯數值逆轉換法及延伸之雙邊拉普拉斯數值逆轉換法來計算暫態時域解。接著分別對於在不同觀察點位置、不同層板厚度比、及施加不同載荷種類之數值運算結果做討論,並將和文獻上之雙層等厚板的靜力解做比較,以驗證本文數值結果之正確性。
英文摘要 In this study, transient elastic waves propagating in a two-layered piezoelectric medium subjected to dynamic mechanical and electrical point loading in the upper layer are investigated. This structure is a two-layered composite laminate constituted by two layers of different thickness of piezoelectric materials. The one-sided and the two-sided Laplace transforms is applied to obtain the shear stresses and the electric displacements in the Laplace transform domain. And then, the Durbin’s method for the one-sided Laplace transform inversion and the extended Durbin’s method for the two-sided Laplace transform inversion are used to carry out the numerical inversion. Finally, the numerical results for different field points, different ratios of thickness, 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 ………………………………………… …Ⅷ
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 …………….……….………………8
第二章 理論基礎………………………………….9
2.1線性壓電材料之控制方程式及本構方程式….9
2.2 拉普拉斯轉換及逆轉換………..………….11
2.3數值逆轉法……..…………………………..12
2.3.1 Durbin 數值逆轉換………………………12
2.3.2 雙邊數值逆轉換………………………….13
第三章 雙異質壓電複合層板內承受單一點載荷之波傳解析..........16
3.1 問題描述…………….……………...…….16
3.2雙異質壓電複合層板內承受單一點載荷之解析………18
3.3雙異質壓電複合層板內承受單一動力點載荷之靜力解析………………………………………………...28
第四章 數值結果與討論………..……….…30
4.1 數值計算說明……………………….…….30
4.2雙異質壓電複合層板內承受單一點載荷之解析…………30
第五章 結論與成果…………………………37
5.1 本文結論…………………………….…….37
5.2本文成果…………………………………….38
5.3尚待研究之方向…………………………….39
參考文獻…………………………………..……41
附錄一 論文精簡版..……………………..…69
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de Hoop, A. T., (1958) Representation theorems for the displacement in an elastic solid and their application to elastodymaic diffraction theory , Doctoral dissertation, Technische hoegschool, Delft.

Durbner, 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.

Ewing, W.M., Jardetzky, W.S., Press, F., (1957) Elastic waves in layered media. McGraw-Hill, New York.

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

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

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.

Müller, G., (1968a) “Theoretical seismograms for some types of point-source in layered media: Part I: Theory,” Z. Geophys 34, 15-35.

Müller, G., (1968b) “Theoretical seismograms for some types of point-source in layered media: Part Ⅱ: Numerical calculations,” Z. Geophys 34, 147-162.

Müller, 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 34, 247-371

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

Ma, C. C. and Huang K. C., (1996b)“Analytical transient analysis of layered composite medium subjected to dynamic in-plane impact loadings” International Journal Solids and Structures 33, 4511-4529.

Ma, C. C. and Lee, G. S., (1999a) “Transient elastic waves propagating in a muti-layered medium subjected to in-plane dynamic loadings. Ⅰ. Theory,” Proceedings of the Royal Society of London 456, 1355-1374.

Ma, C. C. and Lee, G. S., (1999b) “Transient elastic waves propagating in a muti-layered medium subjected to in-plane dynamic loadings. Ⅱ. Numerical calculation and experimental,” Proceedings of the Royal Society of London 456, 1375-1396.

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


Mukunoki, I., Ting, T.C.T., (1980) “Transient wave propagation normal to the layering of a finite layered medium.” International Journal of Solid and Structures 16,239-251.

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.

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

Sun, C.T., Achenbach, J.D., Herrmann, G., (1968) “Continuum theory for a laminated medium.” Journal of Applied Mechanics, Transactions of the ASME 35, 467-475.

Sun, C.T., Chen J.K., (1985) “On the impact of initially stressed composite laminates.” Journal of Composite Materials 19, 490-504.

Tang, Z., Ting, T.C.T.,(1985)“Transient waves in a layered anisotropic elastic medium.” Proceedings of the Royal Society, London. A397,67-85.

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

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。

黃國書 (2011),雙層壓電複合材料受機電點載荷之暫態波傳問題,淡江大學航空太空工程學系碩士班碩士論文。
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