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研究生:魏文彬
研究生(外文):Wen-Bin Wei
論文名稱:壓電材料結合之械形體在面外剪力負載下之機電場分析
論文名稱(外文):The Electro-Mechanical Field of a Piezoelectric Bonded Wedge Under Anti-plane Shear Loading
指導教授:褚晴暉褚晴暉引用關係
指導教授(外文):Ching-Hwei Chue
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:89
中文關鍵詞:壓電體面外剪力梅林轉換楔形結構
外文關鍵詞:piezoelectricshear loadingwedgeMellin transform
相關次數:
  • 被引用被引用:3
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  • 下載下載:148
  • 收藏至我的研究室書目清單書目收藏:0
一般壓電體的材料性質為非等向性,但是當極化方向與楔形結構之軸向方向平行時,會產生橫向等向性的特性。且面內機械場與面外機械場、面內電場會分解,即只有面外機械場會產生電彈耦合效應。本論文利用梅林轉換(Mellin transform),解析單一壓電材料楔形體及兩個等楔形角壓電材料結合而成之楔形體在受到一對面外集中力負載下之機電場。並由所得之機電場進一步探討強度因子、奇異性階數及其所對應之由解析之結果可知,對於單一壓電材料楔形體,面外應力場與面內電位移場互相分解。在所討論的兩種情況中,各場之奇異性階數及角函數皆相同並只與楔形角度有關。藉由所推導出之雙壓電材料楔形體的公式解,我們可以將兩材料之材料性質設為相同,其結果可退化為單一壓電材料的機電場。若將集中負荷之結果作為基本解,運用加權函數的方法可求得任意面外剪力負載下之機電場。本論文之結果也可以應用在含裂
縫之壓電體結構上,如單一壓電材料楔形結構退化為無限域中之半無限長裂縫;雙壓電材料結合之楔形結構退化為兩半無限域間之界面裂縫。此外,若忽略其壓電效應,可退化為純彈性體的問題。
This paper presents the general solutions of antiplane electro-mechanical field for two piezoelectric wedge problems: (1) a piezoelectric wedge subjected to a pair of concentrate forces and free charges; (2) a wedge of equal wedge angles bonded by two dissimilar piezoelectric materials.
Employing the Mellin transform method, the generalized stress, strain, and electrical displacement intensity factors are derived analytically. In addition,the singularity orders and the angular functions expressed in electro-mechanical field can also be obtained.
The accuracies of these solutions have been validated when they are compared to those of some other degenerated problems, which have been widely discussed before. After being reduced to the problem of a semi-infinite antiplane crack in a piezoelectric material or an interface crack in piezoelectric multi-layer materials, the results of the first or second problem can be used as a fundamental solution of other more complicated crack problems by superposition, respectively.
摘要 Ⅰ
英文摘要 Ⅱ
誌謝 Ⅲ
目錄 Ⅳ
圖目錄 Ⅵ
符號說明 Ⅶ
第一章緒論1
§1.1 前言1
§1.2 文獻回顧3
§1.3 研究動機與目的4
§1.4 研究方法5
§1.5 本文架構5
第二章理論分析7
§2.1 壓電體之特性7
§2.1.1 壓電性質7
§2.1.2 本構方程式7
§2.2 壓電體楔形結構9
§2.2.1 強度因子、奇異性階數及角函數10
§2.3 解壓電體楔形結構機電場之方法11
§2.3.1 梅林轉換11
§2.3.2 殘值定理12
第三章基本公式14
§3.1 基本公式14
§3.2 退化情況15
第四章單一壓電材料之楔形結構18
第五章雙等楔形角壓電材料結合之楔形結構36
第六章單一材料壓電體受到一對分佈力之剪力負載58
第七章壓電材料退化為非壓電材料66
第八章結論72
參考文獻74
01.C. J. Tranter, The use of the mellin transform in finding the stress distribution in an infinite wedge. Quarter Journal of Mechanics and Applied Mechanics Vol.1, pp.125-130, 1948.
02.M. L Williams, Pasadena, Calif, Stress Singularities resulting from various boundary conditions in angular corners of plates in extension. Journal of Applied Mechanics 1952.
03.David B. Bogy, Edge-Bonded Dissimilar orthogonal elastic wedges under normal and shear loading. Journal of Applied Mechanics, Transactions of ASME. pp.460-466, 1968.
04.Chien-Ching Ma and Bao-Luh Hour, Analysis of dissimilar anisotropic wedges subjected to anti-plane shear deformation. International Journal of Solids and Structures Vol.25, No. 11, pp.1295-1309, 1989.
05.Y. Eugene Pak. Crack extension force in a piezoelectric material. Journal of applied mechanics, transaction of ASME Vol.57, pp647-653. 1990.
06.Tong-Yi Zhang and J. E. Hack. Mode-Ⅲ cracks in piezoelectric materials. J. Appl. Phys. Vol.71, No.12, pp.5865-5870. 1992.
07.Horacio Sosa, Plane problem in piezoelectric media with defects.International Journal of Solids and Structures Vol.28, N0.4, pp.491-505,1991.
08.S. B. Park and C. T. Sun. Effect of electric field on fracture of piezoelectric ceramics. International Journal of Fracture Vol.70, pp.203-216, 1995.
09.Martin L. Dunn*. The effects of crack face boundary conditions on the fracture mechanics of piezoelectric solids. Engineering fracture mechanics vol.48, No.1, pp.25-39, 1994.
10. Y. Shindo, F. Narita, K. Tanaka, Electroelastic intensification near anti-plane shear crack in orthotropic ceramic strip. Theoretical and Applied Fracture Mechanics Vol.25, pp65-71, 1996.
11. Soon Man Kwon and Kang Yong Lee*, Analysis of stress and electric field in a rectangular piezoelectric body with a center crack under anti-plane shear loading. International Journal of Solids and Structures Vol.37, pp.4859-4869, 2000.
12. Chen Zeng-tao and Yu Shou-Wen. An efficient approach to tackle the anti-plane problems in piezoelectric media. International Journal of fracture Vol.84, L25-L29, 1997.
13. T. C. Wang and X. L. Han, Fracture mechanics of piezoelectric materials.International Journal of Fracture Vol.98, pp15-35, 1999.
14. F. Narita and Y. Shindo, The interface crack problem for bonded piezoelectric and orthotropic layer under antiplane shear loading. International Journal of Fracture Vol.98, pp.87-101, 1999.
15. X.-L. Xu, R.K.N.D. Rajapakse*, Analytical solution for an arbitrarily oriented void/crack and fracture of pizoceramics. Acta mater Vol.47, No.6,pp.1735-1747, 1999.
16. Xian-Fang Li and Tian-You Fan, Semi-infinite anti-plane crack in a piezoelectric material. International Journal of Fracture 102: L55-L60, 2000.
17. X.-L. Xu, R.K.N.D. Rajapakse*, On singularities in composite piezoelectric wedges and junctions. International Journal of Solids and Structures Vol.37, pp.3253-3275, 2000.
18. Ching-Hwei Chue* and Chung-De Chen, Decoupled formulation of piezoelectric elasticity under generalized plane deformation and its application to wedge problems. International Journal of Solids and Structures. 2002.
19. Ching-Hwei Chue* and Chung-De Chen, Antiplane Stress of a Piezoelectric Wedge. Submit to Archive of Applied Mechanics. 2002.
20. Jan J. Tuma, Engineering Mathematics Handbook, Second Enlarged and Revised Edition, 1979.
21. Y. Murakami, Stress intensity factors handbook, The Society of Science,Japan, Vol.2, 1987.
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