# 臺灣博碩士論文加值系統

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 本文旨在利用有限元素法針對壓電材料的動態反應受磁滯效應影響做計算。首先，先在壓電材料本身物理行為的壓電方程式中加入磁滯效應的非線性項「極化（Polarization）P」，並利用Preisach Model 描述磁滯效應。透過此加入磁滯效應項的壓電方程式，利用漢米頓原理（Hamilton’s principle）及變分法的計算，推導出完整的統御方程式，包含了動態方程式（Governing Equation）、連續方程式（Continuous Equation）、邊界條件（Boundary Condition）、以及轉換條件（Transition Condition）等等。最後則以單片壓電致動器（Bender-Unimorph Beam Deflector）為例，透過數值模擬，分別鑑別出半靜態及動態模式時壓電片「極化」的值，並得到動態模式單片壓電致動器受磁滯效應影響的輸出反應。
 This study is devoted to propose a method of finite element technique to account for the hysteresis effect of piezomaterials. To this end, the constitutive equations of a general piezoelectric material are first modified to include the hysteresis effect by adding a polarization term in one of constitutive equations. Based on these modified constitutive equations and employment of Preisach model for hysteresis, the governing equations of the unimorph beam are derived through the utilization of Hamilton’s principle and calculus of variation. In addition, according to the common physical rules, boundary, transition and continuous conditions are next formulated to complement the governing equations. The application of the simple bender-unimorph cantilever beam bas been introduced here to illustrate the hysteresis effect for piezomaterials. Identifying the values of dynamic system of the bender-unimorph cantilever beam, the simulations are finally conducted to show the effectiveness of the proposed modeling techniques and decipher the output response of the piezoelectric beam with consideration of hysteresis effect.
 摘要 ⅠAbstract Ⅱ誌謝 ⅢContents ⅣTable Captions ⅦFigure Captions ⅧNomenclature Ⅹ一、簡介 1二、理論分析 2 2.1 理論建模 2 2.2 描述磁滯效應極化的 Preisach model 2 2.3 鑑別Preisach model 4 2.4 建立第一函數pα’β’之資料庫 5三、單片壓電懸臂樑之應用 7 3.1 物理模型 7 3.2 假設條件 7 3.3 運動方程式 7 3.4 組合有限元素模型 9 3.5 有限元素建模及鑑別 11四、數值鑑別與模擬 12五、結論 131. Introduction 142. Theoretical Analysis 15 2.1 Theoretical Model 16 2.2 Preisach hysteresis model for polarization 16 2.3 Identification of the Preisach model 20 2.4 Creation of database for the first-order function pα’β’ 223. Application to a Simple Bender-Unimorph Cantilever Beam 25 3.1 Physical model 25 3.2 Assumptions 25 3.3 Equations of motion 26 3.4 Assembling the finite element model 29 3.5 Modeling via finite element method and identification 314. Numerical Identification and Simulation 335. Conclusions 35References 36Table titles 38Table 1. Material properties and geometric dimensions of the bender-unimorph beam system.Table 2. The measured displacements for different voltage changes of the quasi-static system.Table 3. The identification results of α1P for the quasi-static system.Table 4. The artificial displacement values for different voltage changes of thedynamic system.Table 5. The identification results of α1P for the dynamic system.Figure captions 43Fig. 1. Elementary hysteresis operator.Fig. 2. Interpretation of Preisach Model.Fig. 3. Triangular region S+(t) when the hysteresis operator γαβ[E3(t)] is in the “up” position.Fig. 4. Triangular region S+(t) when the hysteresis operator γαβ[E3(t)] is in the “down” position.Fig. 5. Hysteresis curves for a piezoceramic actuator.Fig. 6. First-order reversal curves.Fig. 7. Illustration of the hysteresis loop.Fig. 8. Illustration of the region T1(α’,β’) used in the numerical computation ofP(α’,β’) .Fig. 9. The plot of the hysteresis loop of a piezoceramic actuator showing several switching input values α’ and β’ and final input on an ascending branch.Fig. 10. The region S+(t) corresponding to the hysteresis loop shown in Fig. 9.Fig. 11. The plot of the hysteresis loop of a piezoceramic actuator showing several switching input values α’ and β’ and final input on a descending branch.Fig. 12. The region S+(t) corresponding to the hysteresis loop shown in Fig. 11.Fig. 13. A square mesh covering the limiting triangle T.Fig. 14. Square mesh in β-α plane.Fig. 15. Schematic diagram of the cantilever beam with one piezoelectric layer bounded on the top and the input voltage V is applied across the thickness.Fig. 16. Deformation of the ith element of optical beam.Fig. 17. Experimental and identified hysteresis loops in terms of displacement versus electric field E3 for the quasi-static system.Fig. 18. Experimental and identified hysteresis loops in terms of polarization α1P versus electric field E3 for the dynamic system.Fig. 19. Square mesh in β-α plane.Fig. 20. Dynamic time response of piezoelectric unimorph beam tip.簡歷 63
 1. J. J. Shaffer and D. L. Fried, 1970, “Bender-bimorph scanner analysis,” Appl. Opt., 9, pp. 933-937.2. L. K. Lee, 1979, “Piezoelectric bimorph optical beam scannes: analysis and construction,” Appl. Opt., 18, pp. 454-459.3. J. J. Montagu, 1991, Chapter 10 in Optical Scanning, Marshall G. F. (Ed.), Dekker, New York, pp. 525-556.4. J. J. Montagu, 1985, Chapter 5 in Laser Beam Scanning, Optomechanical Devices, Systems, and Data Storage Optics, Marshall G. F. (Ed.), Dekker, New York, pp. 193-219.5. T. Ono, 1990, “Optical beam deflector using a piezoelectric bimorph actuator,” Sensors and Actuators, A, 21-23, pp. 726-728.6. H. S. Tzou and R. Ye, 1994, “Piezothermoelasticity of precision control of piezoelectric systems: theory and finite element analysis,” ASME Journal of Vibration and Acoustics, 116, pp. 489-495.7. R. F. Fung and S. C. Chao, 2000, “Dynamic analysis of an optical beam deflector,” Sensors and Actuators, A 84, pp. 1-6.8. R. F. Fung, S. C. Chao and Y. S. Kung, 2001, “Piezothermaoelastic analysis of an optical beam deflector,” Sensors and Actuators, A 87, pp. 179-187.9. R. Simkovics, H. Landes, M. Kaltenbacher and R. Lerch, 2000, “Finite element analysis of ferroelectric hysteresis effects in piezoelectric transducers,” Ultrasonics Symposium, IEEE, vol. 2 , pp. 1081 -1084.10. R. Simkovics, H. Landes, M. Kaltenbacher and R. Lerch, 1999, “Nonlinear finite element analysis of piezoelectric transducers,” Proc. IEEE Ultrasonics Symposium.11. I. D. Mayergoyz, 1991, Mathematical Models of Hysteresis, New York.12. P. Ge and M. Jouaneh, 1995, “Modeling hysteresis in piezoceramic actuators,” Prec Erng., vol. 17, pp. 211-221.13. P. Ge and M. Jouaneh, 1996, “Tracking Control of a Piezoceramic Actuator,” IEEE Transactions on Control Systems Technology, vol. 4, pp.209-216.14. G. Robert, D. Damjanovic and N. Setter, 2001, ” Preisach distribution function approach to piezoelectric nonlinearity and hysteresis,” Journal of Applied Physics, vol. 90, Iss 5, pp 2459-2464.15. G. Robert, D. Damjanovic, N. Setter, and AV. Turik, 2001, ” Preisach modeling of piezoelectric nonlinearity in ferroelectric ceramics,” Journal of Applied Physics vol 89, Iss 9, pp 5067-5074.16. 馮榮豐，力學能量法：動態系統建模，滄海書局，2000。17. “ IEEE Standard on Piezoelectricity” ANSI/IEEE Std 176-1987, 29 Jan, 198818. E. Kittinger, J. Tichy and W. Friedel, 1986, “Nonlinear piezoelectricity and electrostricition of alpha quartz.” Journal of Applied Physics, vol. 60, No. 4, pp1465-1471.19. R. Lerch, 1988, “Finite element analysis of piezoelectric transducers”, Proc. IEEE Ultrasonic Symposium, pp643-654.20. Catalog of piezoelectric actuators, ValpeyFisher Co.21. 黃友謙，”壓電致動器之動態模擬分析與應用”，私立中原大學機械工程學系碩士學位論文，民國九十年六月。
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 1 壓電致動器的動態與振動模擬分析 2 壓電懸臂樑之精密定位控制設計與實作驗證 3 壓電懸臂樑之有限單元建模與實驗驗證 4 以InversePreisach模型補償磁滯效應在壓電結構上所造成之誤差 5 壓電懸臂樑磁滯效應建模與強健控制器設計及實驗驗證 6 遲滯土壤水分傳輸數值模式之研究 7 含壓電片複合材料旋轉樑動態特性之探討 8 Sn-58Bi、Sn-51In與Sn-37Pb球格陣列構裝的動態疲勞研究及可靠度分析 9 含壓電感應器及制動器之複材薄板有限元素設計 10 雙電極石英晶體微天平共振之提昇能量集中的三維數值模擬 11 壓電致動器對複合樑自由振動之影響 12 部份嵌入壓電材料懸臂樑具焦電效應之動態響應分析 13 新型高分子壓電薄膜之壓電力學行為分析 14 部份嵌入壓電材料懸臂樑之動態響應分析 15 壓電換能器振動模態分析

 1 1.王中一，圖書館營運與最新修正之我國著作權法，東吳法律學報，第十二卷第二期，民國八十九年十二月。 2 3.王國聰，著作權法與圖書館之流通服務關係初探，書苑，第二十七卷，頁23-30，民國八十五年一月。 3 4.古清華，從圖書館及圖書館使用人看圖書館資料庫使用之法律問題，中國圖書館學會會報，第四十九期，頁220。 4 5.余純惠，著作權法對圖書館徵集作業之影響，書府，第十五期，頁74-80，民國八十三年六月。 5 6.宋建成，圖書館法與公共圖書館經營，書藝，第三十七期頁19-26，民國九十年六月。 6 7.何慧玲，學術圖書館文獻傳遞服務之研究，大學圖書館，第五卷第一期頁163-189，民國九十年三月。 7 10.吳嘉生，著作權法中公平使用原則之探討─兼論圖書館之著作權問題，書苑，第二十七期，頁31-38，民國八十五年一月。 8 11.吳嘉生，著作權法與圖書館─以「公平使用原則」為中心，臺北市立圖書館館訊，第十二卷第三期，頁22-27，民國八十四年三月。 9 16.范豪英，著作權法下的圖書館業務問題初探，中國圖書館學會會報，第四十九卷，頁185-189，民國八十一年十二月。 10 17.陳雪華，從數位圖書館的發展兼評＜電子圖書館整合檢索之理論與實作＞「陳昭珍著」，全國新書資訊月刊，第二十四卷，頁24-26，民國八十九年十二月。 11 18.陳俞妏，數位圖書館發展趨勢之探討，國家圖書館館刊，第八十五卷第一期，頁49-60，民國八十五年六月。 12 19.陳家駿，著作權與圖書館經營─以電腦軟體使用與著作權為中心，中國圖書館學會會報，第四十九期，頁201-217，民國八十一年十二月。 13 22.莊麗蘭，圖書館行政之一─圖書館與著作權法，書苑，第二十七期，頁10-22，民國八十五年一月。 14 23.章忠信，著作權法中「散布權」之檢討，萬國法律雜誌，民國九十年四月。 15 24.彭慰，教育部圖書館事業委員會有關圖書館合作之專題研究選介，書苑，第三十六卷，頁1-9，民國八十七年四月。

 1 壓電懸臂樑之精密定位控制設計與實作驗證 2 以InversePreisach模型補償磁滯效應在壓電結構上所造成之誤差 3 軸向移動弦之非線性與智慧型控制器設計 4 人字型凹槽流體軸承之剛性估測 5 四弦型光學讀寫頭之觀測器設計 6 超高速伺服油壓系統與元件響應時間之研究 7 進步型沸水式反應爐負載棄載及汽機跳脫事件之分析研究 8 導光板導光設計之研究 9 菲佐顯微干涉儀研製與應用 10 二維對稱噴流對電子元件熱點衝擊冷卻之熱傳機制研究 11 即時立體視覺物體追蹤系統 12 紊流氣體流經平行渠道含連續粗糙面之流場和共軛熱傳之研究 13 厚件產品保壓過程對於收縮率與殘留應力影響之研究 14 在層流平板流中慣性與熱泳效應影響微粒附著沉積率之研究 15 不同活塞頂面構形之內燃機汽缸數值研究

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