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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/23159完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 張家歐(Chia-Ou Chang) | |
| dc.contributor.author | Ming-Tze Chen | en |
| dc.contributor.author | 陳明澤 | zh_TW |
| dc.date.accessioned | 2021-06-08T04:44:57Z | - |
| dc.date.copyright | 2009-08-12 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-08-03 | |
| dc.identifier.citation | 1. Xu Jun, Li Xin, Ai Hong, “Study on high-performance temperature meter using quartz tuning-fork temperature sensor,” proceedings of the 5th world congress on intelligent control and automation, Hangzhou, P.R.China, pp.3701-3704, 2004
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Hideaki Itoh, Tomoyuki Yuasa, “An Analysis of Frequency of A Quartz Crystal Tuning Fork by Sezawa’s Theory,” 1998 IEEE International Frequency Control Symposium, pp.921-925 9. Hideaki Itoh, Takashi Matsumoto, “An analysis of frequency of a quartz crystal tuning fork by Sezawa's approximation-the effect of clamped position of its base,” 1999 Joint Meeting of the European Frequency and Time Forum and the IEEE International Frequency Control Symposium, pp.494-500, 1999 10. Hideaki Itoh, Yook-Kong Yong, “An Analysis of Frequency of A Quartz Crystal Tuning Fork By Sezawa’s Approximation and Winkler’s Foundation of The Supporting Elinvar Alloy Wire,” 2000 IEEE/EIA International Frequency Control Symposium and Exhibition, pp.420-424 11. Sungkyu Lee, Yangho Moon, Jeongho Yoon, Hyungsik Chung, “Analytical and finite element method design of quartz-tuning fork resonators and experimental test of samples manufactured using photolithography 1-significant design parameters affecting static capacitance C0,” Elsevier, Vacuum 75, pp.57-69, 2004 12. Sungkyu Lee, Yangho Moon, Jaekyu Lee, Jeongho Yoon, Ji-Hoon Moon, Jong-hee Kim, Seung-Hyun Yoo, Hyungsik Chung, “Analytical and finite element method design of quartz-tuning fork resonators and experimental test of samples manufactured using photolithography 2: comprehensive analysis of resonance frequencies using Sezawa’s approximations,” Elsevier, Vacuum 78, pp.91-105, 2005 13. A Castellanos-Gomez, N Agraït, G Rubio-Bollinger, “Dynamics of Quartz Tuning Fork Force Sensors Used in Scanning Probe Microscopy,” IOP Publishing Ltd, Nanotechnology 20, pp.1-8 , 2009 14. Khaled Karrai, Robert D. Grober, “Piezoelectric Tip-Sample Distance Control for Near Field Optical Microscopes,” Appl. Phys. Lett., 66(14), pp.1842-1844, 1995 15. J. C. Brice, “Crystals for Quartz Resonators,” Reviews of Modern Physics, 57(1), 1985 16. Paul Heyliger, “Traction free vibration of layered elastic and piezoelectric rectangular parallelepipeds,” J. Acoust. Soc. Am., 107(3), 2000 17. Raymond D. Mindlin, ”Forced Thickness-Shear and Flexural Vibrations of Piezoelectric Crystal Plates,” Journal of Applied Physics, 23(1), pp.83-88, 1952 18. Robert D. Grober, Jason Acimovic, Jim Schuck, Dan Hessman, Peter J. Kindlemann, Joao Hespanha, A. Stephen Morse, “Fundamental limits to force detection using quartz tuning forks,” Rev. Sci. Instrum., 71(7), pp.2776-2780, 2000 19. Christer Hedlund, Ulf Lindberg, Urban Bucht and Jan Söderkvist, “Anisotropic etching of Z-cut quartz,” J. Micromech. Microeng, 3, pp.65-73, 1993 20. Sungkyu LEE, “Photolithography and selective etching of an array of quartz tuning fork resonators with improved impact resistance characteristics,” The Japan Society of Applied Physics, Vol. 40, Pt. 1, No.8, pp.5164-5167, 2001 21. S. M. Allen and E. L. Thomas, The structure of material, Wiley, 1999 22. Charles Kittel, Introduction to Solid State Physics, 8th ed., Wiley, 2005 23. W. P. Mason, Piezoelectric crystals and their application to ultrasonics, D. Van Nostrand Company, Inc., New York, 1950 24. J. F. NYE, Physical Properties of Crystals, Oxford University Press, 1985 25. Antonio Cazzani and Marco Rovati, “Extrema of Youngs Modulus for Cubic and Transversely Isotropic Solids,” International Journal of Solids and Structures, 40, pp.1713-1744, 2003 26. R. Bechmann, “Elastic and Piezoelectric Constants of Alpha-Quartz,” Physical Review, 110(5), pp.1060-1061, 1958 27. W. G. Cady, Piezoelectricity, McGraw-Hill Book Company, Inc., New York, 1946 28. Jiashi Yang, Analysis of Piezoelectric Devices, World Scientific, 2006 29. Jiashi Yang, An Introduction to The Theory of Piezoelectricity, Springer, 2005 30. Jiashi Yang, The Mechanics of Piezoelectric Structures, World Scientific, 2006 31. Takuro Ikeda, Fundamentals of piezoelectricity, Oxford University Press Inc., New York, 1996 32. 述本正美, 廖詩文, “高頻通訊用晶體振盪器的技術及發展,” 電子與材料雜誌, 第13期, pp.126-131, 2002 33. E. D. Reedy, JR., W. J. Kass, “Finite-element analysis of a quartz digital accelerometer,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 37(5), pp.464-474, 1990 34. Edward B. Magrab, Vibrations of Elastic Structural Members, Springer, 1979 35. Leonard Meirovitch, Principles and Techniques of Vibrations, Prentice Hall, 1997 36. Martin H. Sadd, Elasticity Theory, Applications, and Numerics, Elsevier Inc., 2005 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/23159 | - |
| dc.description.abstract | 本文主要分析(YXl)-88度石英樑以及雙端固定音叉式石英振盪器之共振頻率，首先分析石英樑的共振頻率，利用漢米爾頓定理(Hamilton's Principle)與變分法建立統馭方程式與邊界條件，再使用分離變數法求得特徵方程式、並利用解析解求得特徵值，求得到共振頻率。對於雙端固定音叉式石英振盪器分成同向(in-phase mode)與異向(anti-phase mode)振盪，同向振盪(in-phase mode)可將質量塊視為提摩盛科樑，中間樑為尤拉樑，而對於異向振盪(anti-phase mode)，對質量塊提出新位移場模型，中間樑視為尤拉樑。同向(in-phase mode)與異向(anti-phase mode)振盪兩者都與石英樑方法一樣，利用漢米爾頓定理(Hamilton’s Principle)與變分法建立統馭方程式與邊界條件，再使用分離變數法求得特徵方程式、並利用解析解求得特徵值，求得到共振頻率，所得到的解析解與實驗結果相當符合。利用相同方法分析單音叉的同向(in-phase mode)與異向(anti-phase mode)共振頻率，並建立32.768KHz的理論尺寸。 | zh_TW |
| dc.description.abstract | The thesis is mainly to investigate the resonance frequencies of the (YXl)-88度 quartz beam and the (YXl)-88度 double-ended tuning fork quartz oscillator. First, the resonance frequencies of the quartz beam is analyzed in step one. Governing equations and boundary conditions are obtained by using Hamilton’s Principle and variational principle of mechanics. By applying the separation of variables method, we can derive the eigenequations. The eigenvalues can be obtained by using the analytic solutions. Thus, we can calculate the resonance frequencies of the quartz beam. The modes of the double-ended tuning fork quartz oscillator can be divided into the in-phase mode and the anti-phase mode. For the case of in-phase mode, the proof masses are simulated by using the assumption of Timoshenko beam, and the single beams are simulated by using the assumption of Euler beam. In anti-phase mode, we develop the assumption of anti-phase mode shapes of proof masses, and the single beams are simulated by using the assumption of Euler beam. The problem-solving processes of the in-phase mode and the anti-phase mode are the same as those of the former. Governing equations and boundary conditions are obtained using Hamilton’s Principle and variational principle of mechanics. By applying the separation of variables method, we can derive the eigenequations. The eigenvalues can be obtained by using the analytic solutions. Thus, we can calculate the resonance frequencies of the quartz tuning fork oscillator. The analytic solutions are closely consistent with the experimenting results. By using the same methods, we can analyze the resonance frequencies of the in-plane mode and the out-of-plane mode of the single ending tuning fork oscillator, and derive the theoretical sizes when the frequency is 32.768KHz. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T04:44:57Z (GMT). No. of bitstreams: 1 ntu-98-R96543042-1.pdf: 4893378 bytes, checksum: e5b7558051a688b291132417a1a9dbe3 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | 口試委員會審定書………………………………………………………………………i
誌謝………………………………………………………………………………………ii中文摘要………………………………………………………………………………iii 英文摘要…………………………………………………………………………………iv目錄……………………………………………………………………………………vi 圖目錄…………………………………………………………………………………ix 表目錄…………………………………………………………………………………xv 第一章 導論………………………………………………………………………1 1.1 前言………………………………………………………………………………1 1.2 石英加速規原理…………………………………………………………………2 1.3 文獻回顧…………………………………………………………………………3 1.4 本文目的與章節摘要…………………………………………………………10 第二章 石英材料特性……………………………………………………………12 2.1 石英材料………………………………………………………………………12 2.1.1 晶格對稱性……………………………………………………………………12 2.1.2 對稱操作………………………………………………………………………12 2.1.3 三維晶格類型…………………………………………………………………15 2.1.4 石英晶體的外型………………………………………………………………16 2.2 石英材料常數…………………………………………………………………17 2.2.1 應力與應變……………………………………………………………………17 2.2.2 石英晶體的材料常數…………………………………………………………18 2.2.3 石英晶體的切角設計…………………………………………………………20 第三章 單樑振動………………………………………………………………23 3.1 理想截面之尤拉樑(Euler beam)……………………………………………23 3.1.1 定義座標方向以及長度………………………………………………………23 3.1.2 尤拉樑(Euler beam)之變形假設模型………………………………………24 3.1.3 漢米爾頓定理(Hamilton's principle)…………………………………………28 3.1.4 尤拉樑(Euler beam)之應變能及動能…………………………………………28 3.1.5 尤拉樑(Euler beam)之統馭方程式及邊界條件……………………………30 3.1.6 外型尺寸與頻率的影響………………………………………………………37 3.2 理想截面之提摩盛科樑(Timoshenko beam)………………………………39 3.2.1 提摩盛科樑(Timoshenko beam)之變形假設模型…………………………39 3.2.2 提摩盛科樑(Timoshenko beam)之應變能及動能…………………………40 3.2.3 提摩盛科樑(Timoshenko beam)之統馭方程式及邊界條件………………42 3.2.4 外型尺寸與頻率的影響………………………………………………………49 3.3 溼蝕刻截面之尤拉樑(Euler beam)……………………………………………52 3.3.1 基本假設………………………………………………………………………52 3.3.2 溼式蝕刻之尤拉樑的統馭方程式及邊界條件………………………………52 3.3.3 外型尺寸與頻率的影響………………………………………………………60 3.4 溼式蝕刻之提摩盛科樑(Timoshenko beam)…………………………………62 3.4.1 基本假設………………………………………………………………………62 3.4.2 溼式蝕刻之提摩盛科樑的統馭方程式及邊界條件…………………………63 3.4.3 外型尺寸與頻率的影響………………………………………………………71 第四章 雙端固定音叉式石英振盪器之同向振盪模態…………………………75 4.1 同向振盪之質量塊……………………………………………………………75 4.1.1 同向振盪之質量塊變形假設…………………………………………………75 4.1.2 同向振盪之質量塊的統馭方程式與邊界條件………………………………77 4.2 同向振盪之石英振盪器…………………………………………………………82 4.2.1 同向振盪之統馭方程式與邊界條件…………………………………………82 4.2.2 同向振盪之外型尺寸對頻率的影響…………………………………………95 第五章 雙端固定音叉式石英振盪器之異向振盪模態………………………101 5.1 異向振盪之線性旋轉變形質量塊………………………………………………101 5.1.1 異向振盪之線性旋轉變形質量塊變形假設…………………………………101 5.1.2 異向振盪之線性旋轉變形質量塊統馭方程式及邊界條件…………………104 5.2 異向振盪之線性旋轉變形石英振盪器………………………………………109 5.2.1 異向振盪之線性旋轉變形的統馭方程式與邊界條件………………………109 5.2.2 異向振盪之外型尺寸對頻率的影響…………………………………………116 5.3 異向振盪之非線性旋轉變形質量塊…………………………………………118 5.3.1 異向振盪之非線性旋轉變形質量塊變形假設………………………………118 5.4 異向振盪之非線性旋轉變形石英振盪器………………………………………124 5.4.1 異向振盪之非線性旋轉變形的統馭方程式與邊界條件……………………124 5.4.2 異向振盪之外型尺寸對頻率的影響…………………………………………132 5.5 單音叉式振盪器之異向振盪……………………………………………………137 第六章 結論……………………………………………………………………140 參考文獻……………………………………………………………………………142 附錄A………………………………………………………………………………146 附錄B………………………………………………………………………………157 附錄C………………………………………………………………………………160 附錄D………………………………………………………………………………162 附錄E…………………………………………………………………………………166 附錄F…………………………………………………………………………………168 附錄G………………………………………………………………………………170 附錄H…………………………………………………………………………………173 附錄I…………………………………………………………………………………174 附錄J………………………………………………………………………………176 附錄K………………………………………………………………………………180 作者簡歷……………………………………………………………………………183 | |
| dc.language.iso | zh-TW | |
| dc.subject | 自然頻率 | zh_TW |
| dc.subject | 石英 | zh_TW |
| dc.subject | 振盪器 | zh_TW |
| dc.subject | 漢米爾頓定理 | zh_TW |
| dc.subject | 尤拉樑 | zh_TW |
| dc.subject | 提摩盛科樑 | zh_TW |
| dc.subject | Quartz | en |
| dc.subject | Timoshenko beam | en |
| dc.subject | Euler beam | en |
| dc.subject | Oscillator | en |
| dc.subject | Natural frequency | en |
| dc.title | 單晶石英加速規之自然頻率理論分析 | zh_TW |
| dc.title | Theoretical Analysis of Natural Frequencies of Single-Crystal Quartz Accelerometers | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.coadvisor | 張簡文添(Wen-Tian Chang Chien) | |
| dc.contributor.oralexamcommittee | 張所鋐,謝發華,陳柏志 | |
| dc.subject.keyword | 石英,振盪器,漢米爾頓定理,尤拉樑,提摩盛科樑,自然頻率, | zh_TW |
| dc.subject.keyword | Quartz,Oscillator,Euler beam,Timoshenko beam,Natural frequency, | en |
| dc.relation.page | 183 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2009-08-03 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 應用力學研究所 | zh_TW |
| 顯示於系所單位： | 應用力學研究所 | |
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