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系統識別號 U0002-0808200709475100
中文論文名稱 半雙曲線近似對含裂紋之壓電材料動態特性影響之研究
英文論文名稱 Investigation of Effects on Dynamic Characteristics for Cracked Piezoelectric Materials 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 95
學期 2
出版年 96
研究生中文姓名 謝友誌
研究生英文姓名 Yu-Chih Hsieh
學號 694370510
學位類別 碩士
語文別 中文
口試日期 2007-06-21
論文頁數 82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 半雙曲線近似  壓電材料  振動  裂紋  應力強度因子 
英文關鍵字 quasi-hyperbolic approximation  piezoelectric  vibration  crack  stress intensity factor 
學科別分類 學科別應用科學航空太空
中文摘要 本文利用半雙曲線近似下推導而得的線彈性壓電控制方程式與本構方程式,解析一含有限長裂紋之無窮域壓電材料,於裂紋面上施加反平面應力及平面電位移的簡諧載荷問題。此外,本文亦將此假設應用於靜力問題上,解析一含有限長Yoffe擴展裂紋之壓電材料,於無窮遠處施加反平面應力及平面電位移負載之靜態力問題。本文利用積分轉換法求得含裂紋之壓電材料分別受簡諧載荷與靜力負載時的解析解,並與穩靜態近似下所得到之解作比較。最後針對所求之應力強度因子振幅大小以及相位,做詳細的數值計算與討論。
英文摘要 In this study, the quasi-hyperbolic approximation is used to investigate the dynamic behavior of a crack under the action of anti-plane stresses and in-plane electric displacements in a piezoelectric material. First, the steady-state response of a finite crack subjected to harmonically anti-plane loading and in-plane electric displacement on crack faces is analyzed. Moreover, a moving crack of Yoffe type in piezoelectric materials under remote anti-plane static stresses and in-plane static electric displacements is studied. The stress intensity factors and electric displacement intensity factors are obtained for both problems. Finally, numerical results of the first problem are evaluated and discussed in detail.
論文目次 目 錄
中文摘要 ………………………………………………………………I
英文摘要 ………………………………………………………………II
目錄 ……………………………………………………………………III
圖目錄 …………………………………………………………………V
第一章 緒論 ……………………………………………………………1
1.1 研究動機 …………………………………………………1
1.2 文獻回顧 …………………………………………………4
1.3 內容介紹 …………………………………………………7
第二章 理論基礎 ……………………………………………………8
2.1 麥斯威爾方程式 ……………………………………8
2.2 線彈性壓電控制與本構方程式 ……………………...10
第三章 含裂紋之壓電材料之穩態問題分析 ………………19
3.1 問題描述 ……………………………………………19
3.1 理論解析 ………………………………………………20
3.2 數值計算方法 …………………………………………35
3.3.1 高斯積分法 ………………………………………35
3.3.2 L. U.法 …………………………………………36
3.3.3 數值計算方法應用於求解弗萊德積分方程式 …37
3.4 數值結果與比較 ………………………………………42
第四章 含擴展裂紋之壓電材料受靜態力分析 ……………46
4.1 理論解析 ……………………………………………46
4.2 結果討論 ……………………………………………59
第五章 成果與討論 ……………………………………………60
5.1 本文結論 ………………………………………………60
5.2 本文成果 ………………………………………………60
5.3 尚待研究方向 …………………………………………62
參考文獻 ………………………………………………………………64






















圖 目 錄
圖3-1 含裂紋之壓電材料於不可誘電邊界條件下受簡諧載荷
   的結構示意圖 ……………………………………………68
圖3-2 含裂紋之壓電材料分別採用穩靜態近似以及半雙曲線近似
下, 其應力強度因子的振幅大小關係圖 …………………69
圖3-3 含裂紋之壓電材料分別於採用穩靜態近似以及半雙曲線近似
下, 其相位關係圖 …………………………………………70
圖3-4 含裂紋之壓電材料採用半雙曲線近似下,於不同平面電位移
負載所得到的應力強度因子振幅大小關係圖 ……………71
圖3-5 含裂紋之壓電材料採用半雙曲線近似下,於不同平面電位移
負載所得到的相位關係 ……………………………………72
圖3-6 Chen and Yu (1998) 於不同平面電位移負載所得到的應力強
度因子振幅大小關係圖 ……………………………………73
圖3-7 Chen and Yu (1998) 於不同平面電位移負載所得到的相位關
係圖 …………………………………………………………74
圖3-8 一般彈性材料受簡諧載荷時的應力強度因子的振幅大小關係
圖 ……………………………………………………………75
圖3-9 Loeber and Sih(1968) 一含有限長裂紋之無窮域純彈性材料,受一反平面動力載荷的應力強度因子振幅大小關係…76
圖3-10 含裂紋之壓電材料於半雙曲線近似下,於較大振動頻率時所
得到的應力強度因子振幅大小關係圖 ……………………77
圖3-11 含裂紋之壓電材料於半雙曲線近似下,於較大振動頻率時所
得到的相位關係圖 …………………………………………78
圖3-12 含裂紋之壓電材料分別採用穩靜態近似以及半雙曲線近似
下,受較大振動頻率時的應力強度因子振幅大小關係
圖 ……………………………………………………………79
圖4-1 含擴展裂紋之壓電材料於無窮遠處受力示意圖 …80
圖4-2 無裂紋之壓電材料於無窮遠處受力示意圖 ………81
圖4-3 含有限長裂紋之無窮域壓電材料受反平面均佈應力
及平面電位移負載示意圖 ……………………………82
參考文獻 參考文獻

Benjeddou, A. and Deü, J. F., (2002) “A two-dimensional closed-form solution for the free-vibrations analysis of piezoelectric sandwich plates,” International Journal of Solids and Structures, Vol. 39, pp. 1463-1486.

Benjeddou, A., Deü, J. F. and Letombe, S., (2002) “Free vibrations of simply-supported piezoelectric adaptive plates: an exact sandwich formulation,” Thin-Walled Structures, Vol. 40, pp. 573-593.

Chen, W. Q., Liang, J. and Ding, H. J., (1997) “Exact three dimensional analysis of bending problem of piezoelectric composite thick rectangular plate,” Chinese Journal of Composite Material, Vol. 14, pp. 108-115.

Chen, Z. T. and Yu, S. W., (1997a) “Antiplane Yoffe crack problem in piezoelectric materials, “International Journal of Fracture, Vol. 84, L41.

Chen, Z. T. and Yu, S. W., (1997b) “Antiplane dynamic fracture mechanics in piezoelectric materials, “ International Journal of Fracture, Vol. 85, L3-L12.

Chen, Z. T. and Yu, S. W., (1998) “Anti-plane vibration of cracked piezoelectric materials,“ Mechanics Research Communication, Vol. 25, No.3, pp. 321-327.

Ding, H. J., Xu, R.Q. and Chen, W.Q., (2002) “Free vibration of transversely isotropic piezoelectric circular cylindrical panels,” International Journal of Mechanical Sciences, Vol. 44, pp. 191-206.

Dokmeci, M. C., (1980) “Recent advances: vibrations of piezoelectric crystals,” International Journal of Endineering Science, Vol. 18, pp. 431-448.
Fan, J. L. and Ye, J. Q., (1990) “An exact solution for the statics and dynamics of laminated thick plate with orthotropic layers,” International Journal of Solids and Structures, Vol. 26, pp. 655-662.

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

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

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

Loeber, J. F. amd Sih, G. C. (1968) “Diffraction of Antiplane Shear Waves by a Finite Crack,” The Journal of Acoustic Society of America, Vol. 44, pp.90-98.

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

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

McMeeking, R. M., (1989a) “ Electrostricitive stress near crack-like flaws,” Zeitschrift f r Angewandte Mathematik und Physik, Vol. 40, pp. 615-627.

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, Vol. 33, pp. 85-96.

Mindlin, R. D., (1952) “Forced thickness-shear and flexural vibrations of piezoelectric crystal plates,” Journal of Applied Physics, Vol. 23, pp. 83-88.
Mindlin, R. D., (1984) “Frequencies of piezoelectrically forced vibrations of electroded, doebly rotated quartz plates.” International Journal of Solids and Structure, Vol. 20, pp.141-157.

Pak, Y. E., (1990) “Crack extension force in a piezoelectric material,” Journal of Applied Mechanics, Vol. 57, pp. 647-653.

Pak, Y. E., (1992) “Linear electroelastic fracture mechanics of piezoelectric material,” International Journal of Fracture, Vol. 54, pp. 79-100.

Pak, Y. E. and Goloubeva, (1996) “Electroelastic properties of cracked piezoelectric material under longitudinal shear,” Mechanics of Materials, Vol. 24, pp. 287-303.

Park, Y. E. and Sun, C. T., (1995a) “Effect of electric field on fracture of piezoelectric ceramics,” International Journal of Fracture, Vol. 70, pp. 203-216.

Park, Y. E. and Sun, C. T., (1995b) “Fracture criteria for piezoelectric ceramics,” J. Am. Ceram. Soc. Vol. 78, pp. 1475-1480.

Parton, V. Z., (1976) “Fracture mechanics of piezoelectric materials.” Acta Astronaut, Vol. 3, pp. 671-683.

Parton, V. Z. and Boriskovsky, V. G., (1989) “Dynamic Fracture Mechanics,” Vol. 1, Hem isphere Publishing Corporation, New York.

Suo, Z. C., Kuo, M. D., Barnett, M. and Willis, J. R., (1992) “Fracture mechanics of piezoelectric ceramics,” Journal of the Mechanics and Physics of Solids, Vol. 40, pp. 739-765.


Tirsten, H. F., (1969) Linear piezoelectric plate viberations. Plenum Press, New York.

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

Vel, Senthil S., Mewer, R.C. and Batra, R.C., (2004) “Analytical solution for the cylindrical bending vibration of piezoelectric composite plates,” International Journal of Solids and Structures, Vol. 41, pp. 1625-1643.

Wu, Y. C. and Heyliger. P., (2001) ” Free vibration of layered piezoelectric spherical caps,” Journal of Sound and Vibration, Vol. 245, pp. 527-544.

Yoffe, E. H., (1951) “The moving Griffith crack,” Philosophical Magazine, Vol. 42, pp. 739-750.

Zhang, T. Y. and Tong, P., (1996) “Fracture mechanics for mode III crack in a piezoelectric material,” International Journal of Solids and Structures, Vol. 33, pp. 343-359.

Zhong, Z. and Meguid, S. A., (1997) “Interfacial debonding of a circular inhomogeneity in piezoelectric materials,” International Journal of Solids and Structures, Vol. 34, pp. 1965-1984.

郭詮 (2004) ”含裂紋壓電材料受簡諧載荷之動態解析,” 淡江大學航太工程學系碩士論文

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