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研究生:張聖心
研究生(外文):Sheng-Hsin Chang
論文名稱:以雙片壓電懸臂樑進行材料的黏彈性量測
論文名稱(外文):Quantitative Determination of Material Viscoelasticity Using a Piezoelectric Cantilever Bimorph Beam
指導教授:馮榮豐馮榮豐引用關係
指導教授(外文):Rong-Fong Fung
學位類別:碩士
校院名稱:國立高雄第一科技大學
系所名稱:機械與自動化工程所
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:2002
畢業學年度:90
語文別:英文
論文頁數:49
中文關鍵詞:奈米技術黏彈性量測壓電元件
外文關鍵詞:nanotechnologydetermination of viscoelasticitypiezoelectric
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本文推導出具有端點質量之雙壓電片懸臂樑,它的下方聯繫一個由勁度與阻尼並聯所組成的黏彈性材料。藉由特徵值問題與頻譜分析,可得到端點質量、材料勁度與共振頻率,以及頻譜與材料阻尼值,完整的關係式。依據上述關係式,我們得知共振頻率,隨著材料勁度的增加而提高、隨著端點質量的增加而降低,頻譜振幅隨著阻尼值的增加而降低,等重要的現象。分析結果顯示,可藉由量測懸臂樑的共振頻率與頻譜分析,提出一套簡單量測材料黏彈性的技術。因為懸臂樑的行為與其幾何尺度有關,故本文中所提出的方法,可以供微系統之機械性質量測設備,如進行細胞或生醫材料量測等。


The objective of this paper is to formulate the governing equation of a cantilever bimorph beam associated with a tip mass in contact with a viscoelastic material, which is modeled by a stiffness and a damper in parallel. From the eigenvalue problem, we can obtain the resonant frequencies as functions of the tip mass and material stiffness. The relation between the spectrum and material damping is established by the half-power bandwidth. It is found that the resonant frequencies increase as the material stiffness increases or the tip mass decreases, and the spectrum decreases by increasing the damping. From the analytic results, a cantilever could provide a technique to assess material viscoelasticity by simple measurements of the resonant frequency and the spectrum. Since the cantilever’s behavior scales with its geometry, the device can be designed specifically for mechanical measurement of a microscopic system such as living cells and biomaterials.


Contents
摘要i
Abstractii
誌謝iii
Contentsiv
Table Captionvi
Figure Captionvii
Nomenclatureix
1. Introduction1
2. Dynamic Model Development2
2.1 The Physical Model2
2.2Equations of Motion2
2.3 Kinetic and Strain Energies3
2.4 Hamilton’s Principle5
2.5Discussion6
2.6 Eigenvalue Problem7
2.7Comparison10
2.8A Simple Case and Sensitivity Analysis11
3. Damping Determination from Half-Power Bandwidth12
4. Finite Element Method13
5. Numerical Results15
5.1 Determination of Material Stiffness15
5.2 Determination of Material Damping17
6. Conclusions18
References18
Appendix A21
Appendix B22
Appendix C24


References1. Binning, G., Quate, C. F. and Gerber, C., 1986, “Atomic Force Microscope”, Physical Review Letters, 56, pp. 930-933.2.Fung, R. F. and Huang, S. C., 2001, “Dynamic Modeling and Vibration Analysis of the Atomic Force Microscope”, ASME Journal of Vibration and Acoustics, 123, pp. 502-509.3.Finot, E., Thundat, T., Lesniewska, E. and Goudonnet, J. P., 2001, “Measuring Magnetic Susceptibilities of Nanogram Quantities of Materials Using Microcantilevers, Ultramicroscopy, 86, pp. 175-180.4.Porter, T. L., Eastman, M. P., Pace, D. L. and Bradley, M., 2001, “Sensor Based on Piezoresistive Microcantilever Technology”, Sensors and Actuators A 88, pp. 47-51.5.Ji, H. F., Hansen, K. M., Hu, Z. and Thundat, T., 2001, “Detection of pH Variation Using Modified Microcantilever Sensors”, Sensors and Actuators B 72, pp. 233-238.6.Wang, L., 1999, “The Role of Damping in Phase Imaging in Tapping Mode Atomic Force Microscopy”, Surface Science, 429, pp. 178-185.7.Kester, E., Rabe, U., Presmanes, L., Tailhades, P. and Arnold, W., 2000, “Measurement of Young’s Modulus of Nanocrystalline Ferrites with Spinel Structures by Atomic Force Acoustic Microscopy”, Journal of Physics and Chemistry of Solids, 61, pp. 1275-1284.8. Guo, N., Gawley, P. and Hitchings, D., 1992, “The Finite Element Analysis of the Vibration Characteristics of Piezoelectric Discs”, Journal of Sound and Vibration, 159, pp. 115-138.9. Fung, R. F., Yao, C. M. and Tseng, C. R., 1999, “Dynamic Analysis of a Bimodal Ultrasonic Motor with Initially Stressed Force onto the Rotor”, Sensors and Actuators A, 72, pp. 115-138.10.Meirovitch, L., 2001, Fundamentals of Vibrations, McGraw-Hill, International Edition, Singapore.11.Coughlin, M. F., Stamenovic, D. and Smits, J. G., 1997, “Determining Spring Stiffness by the Resonance Frequency of Cantilevered Piezoelectric Bimorphs”, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 44(4), pp. 730-732.12.Amelio, S., Goldade, A. V., Rabe U., Scherer V., Bhushan B. and Arnold W., 2001, “Measurements of Elastic Properties of Ultra-thin Diamond-like Carbon Coatings Using Atomic Force Acoustic Microscopy”, Thin Solid Films, 392, pp. 75-84.13.Rabe U., Janser K. and Arnold W., 1996, “Vibrations of Free and Surface-coupled Atomic Force Microscope Cantilevers: Theory and Experiment”, Review of Scientific Instruments, 67(9), pp. 3281-3293.14.Nashif, A. D., Jones, D. I. G. and Henderson J. P., 1984, Vibration Damping, Chapter 4, John Wiley & Sons.15.Bert, C. W., 1973, “Material Damping: An Introductory Review of Mathematical Models, Measures and Experimental Techniques”, Journal of Sound and Vibration, 29, pp. 129-153.16.Reddy, J. N., 1993, An Introduction to the Finite Element Method, Chapters 14, Second Edition, McGraw-Hill International editions.17.Balamurugan, V. and Narayanan, S., 2002, “Finite Element Formulation and Active Vibration Control Study on Beams Using Smart Constrained Layer Damping (SCLD) Treatment”, Journal of Sound and Vibration, 249(2), pp. 227-250.

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