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研究生:曾泓晟
研究生(外文):Hung-Cheng Tseng
論文名稱:壓電材料磁滯效應之微觀建模與實驗驗證
論文名稱(外文):Construction of a Micro- Hysteresis Model for Piezomaterials and Experimental Verification
指導教授:黃健生黃健生引用關係
指導教授(外文):Jeng-Shen Huang
學位類別:碩士
校院名稱:中原大學
系所名稱:機械工程研究所
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:2003
畢業學年度:91
語文別:中文
論文頁數:74
中文關鍵詞:有限元素法壓電材料磁滯效應
外文關鍵詞:hysteresisfinite element methodpiezomaterial
相關次數:
  • 被引用被引用:4
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  • 下載下載:43
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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 Ⅰ
Abstract Ⅱ
誌謝 Ⅲ
Contents Ⅳ
Table Captions Ⅶ
Figure Captions Ⅷ
Nomenclature 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 13
1. Introduction 14
2. 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’ 22
3. 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 31
4. Numerical Identification and Simulation 33
5. Conclusions 35
References 36
Table titles 38
Table 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 the
dynamic system.
Table 5. The identification results of α1P for the dynamic system.
Figure captions 43
Fig. 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 of
P(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, 1988
18. 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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