微型矽晶圓環陀螺儀的振動分析

Wen-Chang Yang; 楊文彰

請用此 Handle URI 來引用此文件： http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/36796

完整後設資料紀錄

DC 欄位	值	語言
dc.contributor.advisor	張家歐
dc.contributor.author	Wen-Chang Yang	en
dc.contributor.author	楊文彰	zh_TW
dc.date.accessioned	2021-06-13T08:16:25Z	-
dc.date.available	2005-07-27
dc.date.copyright	2005-07-27
dc.date.issued	2005
dc.date.submitted	2005-07-19
dc.identifier.citation	[1] Brantley, W. A. 1973.“Calculated Elastic Constants for Stress Problems Associated with Semiconductor Devices”, J. Appl. Phys. Vol. 44, No. 1, pp.534-535. [2] Bickford, W. B. and Reddy, E. S. 1985.“On the In-Plane Vibrations of Rotating Ring”, J. Sound Vib. 101(1), pp.13-22. [3] Cazzani, A. and Rovati, M. 2003.“Extrema of Young’s Modulus for Cubic and Transversely Isotropic Solids”, International Journal of Solids and Structures. 40, pp.1713-1744. [4] Eley, R. Fox, C. H. J. and McWillian, S. 2000.“Coriolis Coupling Effects on the Vibration of Rotating Ring”, J. Sound Vib.238(3), pp.459-480. [5] Eley, R., Fox, C. H. J. and McWillian, S. 1999.“Anisotropy Effects on the Vibration of Circular Ring Made from Crystalline Silicon”, J. Sound Vib.228(1), pp.11-35. [6] Fox, C. H. J. 1990.“A Simple Theory for the Analysis and Correction of Frequency Splitting in Slightly Imperfect Rings”, J. Sound Vib.142(2), pp.227-243. [7] Gallacher, B. J., Burdess, J. S., Harris, A. J. and McNie, M. E.2001.“Principles of a Three-Axis Vibrating Gyroscope”, IEEE Transations on Aerospace and Electronic Systems. Vol. 37, No. 4, pp.1333-1343. [8] Harris, A. J., Burdess, J. S., Wood, D., Langford, R., Walliams, G., Ward, M. C. L. and McNie, M. E. 1998.“Issues Associated with the Design, Fabrication and Testing of a crystalline Silicon Ring Gyroscope with Electromagnetic Actuation and Sensing”, J. Micromech. Microeng. 8, pp.284-291. [9] Hayes, M. and Shuvalov, A. 1998.“On the Extreme Values of Young’s Modulus, the Shear Modulus, and Poisson’s Ratio for Cubic Materials”, ASME Journal of Applied Mechanics, Vol. 65, pp.786-787. [10] He, G. and Najafi, K. 2002.“A Single-Crystal Silicon Vibrating Ring Gyroscope.”, Proc. The 15th IEEE Int. Conf. on Micro Electro Mechanical Systems, Las Vegas, Jan. 20-24, pp.718-721. [11] Kelly, A., Groves, G. W. and Kidd, P. 2000., Crystallography and Crystal Defects, New York, John Wiley and Sons. [12] Kim, W. 2002.“Free Non-Linear Vibration of a Rotating Thin Ring with the In-Plane and Out-of-Plane Motions”, J. Sound Vib.258(1), pp.167-178. [13] Kim, J., Cho, D. and Muller, R S. 2001.“Why Is (111) Silicon a Better Mechanical Material for Mems”, Proc. The 11th Transducers Int. Conf. on Solid-State Sensors and Actuators, Munich, Germany, June. pp.662-665. [14] Love, A. E. H. 1927., A Treatise on the Mathemtical Theory of Elasticity, New York, McGraw-Hill. [15] Nayfeh, A. H. 1973., Introduction to Perturbation Techniques, New York, John Wiley and Sons. [16] Nikrayesh, 1988., Computer-aided analysis of mechanical systems, Ptentice-Hall. [17] Nye, J. F. and S. F. R. 1957., Physical Properties of Crystals, New York, Oxford. [18] Rao, S. S. and Sundararajan, V. 1969.“In-Plane Flexural Vibrations of Circular Rings”, Transction ASME Journal of Applied Mechanics, Sept, pp.620-625. [19] Royer, D. 1996. Elastic Waves in Solids I, Spring. [20] Shuvalov, L. A. 1981. Modern Crystallography IV：Physical Properties of Crystals, New York, Spring. [21] Walpoe, L. J. 1986.“The elastic Shear Modui of Cubic Crystal”, J. Phys. D：Appl. Phys. 19, pp.457-462. [22] Washizu, K. 1982. Variational Methods in Elasticity and Plasticity, New York, Oxford. [23] Wortman, J. J. and Evans, R. A. 1965.“Young’s Modulus, Shear Modulus, and Poisson’s Ratio in Silicon and Germanium”, J. Appl. Phys. Vol. 36, No. 1, pp.153-156. [24] 李信坤, 2003, 微環型諧振式陀螺儀之動力分析, 國立台灣大學應用力學研究所碩士論文. [25] 賴威凡, 2004, 三維諧振式環型微陀螺儀理論與分析, 國立台灣大學應用力學研究所碩士論文. [26] 許書豪, 2005, 三維諧振式環型微陀螺儀之結構設計與理論分析, 國立台灣大學應用力學研究所碩士論文. [27] 張福學, 2001, 現代壓電學上冊, 科學出版社
dc.identifier.uri	http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/36796	-
dc.description.abstract	本文是探討將矽晶圓非等向性的材料性質引入到圓環的頻率推導中，觀察非等向性對圓環自然振動頻率造成的影響，之後比較有無項對振動頻率的影響。比較由非等向性(100)與等向性(111)晶圓製造的圓環因為非等向性所產生的頻率差異，由於非等向性造成(100)的與模態的頻率不相同，因此考慮新式的圓環將兩個模態的頻率調整成相同，以確保引入角速度後能將模態激發起來，以降低量測角速度時的誤差。接著引入角速度並且利用電極激發圓環，藉由Lagrange’s equation推導出運動方程式，考慮兩種類型的驅動電壓去驅動圓環振動，使用數值解的方式解出(100)與(111)的圓環振幅大小，並且探討不同電壓與角速度值對於振幅大小的影響，之後利用微擾法(perturbation method)解出振幅比值與角速度的解析解。使用套裝軟體去模擬(100)與(111)圓環的振動頻率，並與推導的理論值互相比較，最後模擬加入支撐架的圓環，並與未加入支撐架的圓環的振動頻率做一比較。	zh_TW
dc.description.provenance	Made available in DSpace on 2021-06-13T08:16:25Z (GMT). No. of bitstreams: 1 ntu-94-R92543001-1.pdf: 1072457 bytes, checksum: d3db803c39984bea1698b66b6264613c (MD5) Previous issue date: 2005	en
dc.description.tableofcontents	摘要.............................................I 目錄.............................................II 圖目錄...........................................V 表目錄...........................................X 第1章導論....................................1 1.1 前言....................................1 1.2 文獻回顧................................1 1.3 本文目的與內容..........................4 第2章矽晶圓非等向性推導......................6 2.1 矽晶圓對稱型驗證.......................6 2.2 (100)與(111)晶格面的勁度矩陣............11 2.2.1 (100)晶格面的勁度矩陣...................11 2.2.2 (111)晶格面的勁度矩陣...................18 第3章圓環的自由振動分析......................26 3.1 圓環模型................................26 3.2 應變能與動能............................28 3.2.1 應變能..................................28 3.2.2 動能....................................29 3.3 運動方程式..............................30 3.3.1 模態的頻率.............................33 3.3.2 模態的頻率.............................37 3.4 數值計算................................42 3.4.1 (100)圓環自然頻率.......................42 3.4.2 (111)圓環自然頻率.......................43 3.5 新式設計的圓環..........................45 第4章電極驅動................................52 4.1 運動方程式..............................52 4.2 振幅數值解..............................57 4.2.1 第一型施加電壓..........................57 4.2.1.1 圓環的振幅..............................58 4.2.1.2 圓環的振幅..............................62 4.2.2 第二型施加電壓..........................66 4.2.2.1 圓環的振幅..............................67 4.2.2.2 圓環的振幅..............................69 4.3 電壓與振幅比值..........................72 4.3.1 第一型施加電壓..........................72 4.3.2 第二型施加電壓..........................75 4.4 振幅解析解..............................77 第5章模擬分析................................88 5.1 模擬結果................................88 5.1.1 圓環尺寸與元素類型......................88 5.1.2 (100)圓環模擬...........................89 5.1.3 (111)圓環模擬...........................92 5.2 支撐架..................................96 第6章結論....................................102 參考文獻.........................................105 附錄A............................................109 附錄B............................................111 附錄C............................................113 附錄D............................................139 附錄E............................................141 附錄F............................................144
dc.language.iso	zh-TW
dc.subject	矽晶	zh_TW
dc.subject	陀螺儀	zh_TW
dc.subject	gyroscope	en
dc.subject	silicon	en
dc.title	微型矽晶圓環陀螺儀的振動分析	zh_TW
dc.title	Vibrating analysis of silicon ring-type micro gyroscope	en
dc.type	Thesis
dc.date.schoolyear	93-2
dc.description.degree	碩士
dc.contributor.oralexamcommittee	周元訪,謝發華,張簡文添
dc.subject.keyword	矽晶,陀螺儀,	zh_TW
dc.subject.keyword	silicon,gyroscope,	en
dc.relation.page	146
dc.rights.note	有償授權
dc.date.accepted	2005-07-20
dc.contributor.author-college	工學院	zh_TW
dc.contributor.author-dept	應用力學研究所	zh_TW
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