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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 張家歐 | |
dc.contributor.author | Szu-Chia Lin | en |
dc.contributor.author | 林思嘉 | zh_TW |
dc.date.accessioned | 2021-06-08T00:42:47Z | - |
dc.date.copyright | 2015-08-28 | |
dc.date.issued | 2015 | |
dc.date.submitted | 2015-08-14 | |
dc.identifier.citation | [1] Rayleigh, L, 1881, “On the Infinitesimal Bending of Surfaces of Revolution,” Proc. Math. Soc., London, Vol.13, pp. 4-16. [2] Love, A. E. H., 1888, “On th Small Free Vibrations and Deformation on Thin Elastic Shells,” Phil. Transactions Roy. Soc., A179, pp. 491-546. [3] Bryan, G. H., 1890, “On the Beats in the Vibrations of a Revolving Cylinder or Bell,” Proc. Cambridge Philos. Soc., Vol. VII, Nov. 24, pp. 101-111. [4] Quick, W. H, 1964, “Theory of the Vibrating String as an Angular Motion Sensor,” Transactions ASME, J. Appl. Mech., pp. 523-534 [5] Friedland, Bernard and Maurice F. Hutton,1978, “Theory and Error Analysis of Vibrating-Member Gyroscope,” IEEE Transactions on Automatic Control, Vol. AC-2345, No. 4, pp. 545-556 [6] Washizu, K., 1980, Variational Methods in Elasticity and Plasticit, Pergamon Press Ltd., 3rd. [7] Niordson, F. I., 1985, Shell Theory, North Holland, Amsterdam. [8] Chang, C. O., Hwang , J. J., and Chou, C. S., 1996, “Modal Procession of a Rotating Hemispherical Shell,” International Journal of Solids and Structures, Vol. 33, No. 19, pp. 2739-2757. [9] 謝發華,2001,壓電驅動半圓球殼振動陀螺儀原理與誤差分析,博士論文,台灣大學應用力學研究所。 [10] 黃正吉,1993,半圓球殼諧振陀螺儀的動力分析,博士論文,台灣大學應用力學研究所。 [11] Gallacher, B. J., 2012, “Principles of a Micro-Rate Integrating Ring Gyroscope,” IEEE Transactions om Aerospace and Electronnic Systems, Vol. 48, No. 1. [12] Gallacher, B. J., Burdess, J. S., Harris, A. J., Rickard, A., and King, D.O., 2005, “Electrostatic correction of structural imperfections present in a microring gyroscope,” Journal of Microelectromechanical Systems, Vol. 14, Issue. 2, pp. 221-234. [13] Seong-Yoel Choia, Ji-Hwan Kimb,2010, “Natural frequency split estimation for inextensional vibration of imperfect hemispherical shell”, Journal of Sound and Vibration, Vol. 330, Issue. 9, pp. 2094-2106. [14] 陳劭詮,2014,諧振半球殼缺陷分析與控制,碩士論文,台灣大學應用力學研究所。 [15] 王文呈,2014,諧振半球殼質量補償模擬與分析,碩士論文,台灣大學應用力學研究所。 [16] 翁銘宗,2015,諧振半球殼陀螺儀的設計與質量瑕疵的修正,碩士論文,台灣大學應用力學研究所。 | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/17736 | - |
dc.description.abstract | 半圓球殼陀螺儀之主要原件為半圓球殼,其毛胚在製造過程中多少都會伴隨著雜質或氣泡所產生密度的不均勻性,以及加工產生的半徑或厚度等參數的誤差,此時半圓球殼即呈瑕疵狀態。理想球殼相同自然頻率的兩個不同模態會因這些瑕疵產生自然頻率分歧(frequency bifurcation)。本文利用漢彌頓原理以及Niordson所採用的雷利近似解之方法推導出理想半圓球殼的運動方程式以及質量分布不均勻半圓球殼的運動方程式,觀察瑕疵存在對於半圓球殼頻率與特徵向量的影響,並且修正此頻率分歧之現象。 為了建立修正頻率分岐的理論模型,首先規劃有效微調質量修正方法,謝發華[9]曾利用驅動與感測模態做修正,本文則利用在半圓球殼之低頻特徵向量方向上做修正。選擇兩分岐自然頻率的低頻所對應的特徵向量與球殼的交線點做雷射質量燒蝕的位置。本文證明在特徵向量上的點做修正是不會產生耦合效應,使特徵向量在不斷的燒蝕過程中保持不變。由兩模態振幅來繪出Lissajous圖,藉調整激發與感測電極的角度及由Lissajous圖可判斷特徵向量之方向。由理論推導出的燒蝕質量與兩分岐自然頻率的函數關係公式可作為實務修正的參考依據。 | zh_TW |
dc.description.abstract | The major component of the hemispherical resonator gyroscope is the hemispherical shell (HS). More or less the voids, bubbles, and impurities are produced in the forming process of blanks which causes the non-uniformity in density,and it is inevitable to suffer the geometric errors in the manufacturing process of the HS. These situations cause the HS to be imperfection. In this thesis Hamilton principle and Lore Rayleigh’s approximate solution are employed to derive the equations of motion of both the ideal HS and the imperfection HS. The effect of the imperfection on the frequency bifurcation and eigenvectors is investigated. In order to establish the theoretical model of correcting the frequency bifurcation Dr. Fa-Hua Hsieh [9] proposed the method of mass-trimming on the driving and sensing modes. Here a method of mass-trimming on the eigenvectors is invented. The positions for mass-trimming are located at the intersections of the eigenvector, corresponding to the lower one of the two bifurcated frequencies, and the great circle of the shell. It is proved that mass-trimming on the eigenvector eliminate the coupling effect, that is, eigenvector keeps unchanging during the successive corrections of mass trimming. The amplitudes of the modes are used to plot the Lissajous figure. By adjusting the angular positions of the driving and sensing electrodes and the judgment from the Lisajous figure the eigenvector can be determined. The derived equation which relates the amount of mass to be trimmed and the bifurcated frequencies can be used as reference for frequency correction. | en |
dc.description.provenance | Made available in DSpace on 2021-06-08T00:42:47Z (GMT). No. of bitstreams: 1 ntu-104-R02543021-1.pdf: 1868560 bytes, checksum: 84ced20c636c9e1492b5259d92af86a4 (MD5) Previous issue date: 2015 | en |
dc.description.tableofcontents | 致謝 1 中文摘要 2 Abstract 3 目錄 4 圖目錄 7 第1章 緒論 11 1.1 前言 11 1.2 文獻回顧 12 1.3 論文架構 14 第2章 Niordson線性薄殼理論[9] 15 2.1 抗變向量(Contravariant vector)與協變(Covariant vector)向量 15 2.2 座標系統 16 2.2.1 二維曲面座標系統 17 2.2.2 三維簡正座標系統 18 2.2.3 球座標系統 20 2.3 Niordson 薄殼基本理論 23 2.3.1 應變量與位移 24 2.3.2 虎克定律與應變能 25 2.3.3 薄膜應力張量與彎矩張量 28 第3章 半圓球殼諧振陀螺儀運動方程式[9] 29 3.1 漢彌頓原理 29 3.1.1 半圓球殼之旋轉殼動能 30 3.1.2 半圓球殼之應變能 35 3.1.3 外部附載 39 3.1.4 邊界條件 41 3.2 理想半球殼陀螺儀運動方程式 43 3.2.1 雷利近似解 43 3.2.2 感測係數 47 3.2.3 勁度係數 51 3.2.4 感測方程式 53 3.2.5 自然頻率 56 第4章 瑕疵半圓球殼之分析 57 4.1 單瑕疵量 57 4.1.1 單瑕疵之特徵值與特徵向量 57 4.1.2 單瑕疵之數值計算 61 4.1.3 單瑕疵之特殊位置討論與說明 63 4.2 雙瑕疵量 65 4.2.1 雙瑕疵之特徵值與特徵向量 65 4.2.2 雙瑕疵之數值計算 68 4.3 多瑕疵量 73 4.3.1 多瑕疵量之特徵值與特徵向量 73 4.4 初始條件之物理意義 76 第5章 半圓球殼瑕疵量修正 79 5.1 單瑕疵之修正 80 5.1.1 單瑕疵修正之理論 80 5.1.2 單瑕疵修正之數值計算 85 5.2 雙瑕疵之修正 88 5.2.1 雙瑕疵修正之理論 88 5.2.2 雙瑕疵修正之數值計算 91 5.3 多瑕疵之修正 97 5.3.1 多瑕疵修正之理論 97 5.3.2 多瑕疵修正之數值計算 99 5.4 質量微調之方向 101 5.4.1 單瑕疵量特徵向量之驗證 101 5.4.2 雙瑕疵量特徵向量之驗證 105 5.4.3 多瑕疵量特徵向量之驗證 110 5.5 修正量與分歧頻率之關係 111 5.6 瑕疵量修正方法 116 第6章 結論與未來展望 120 6.1 結論 120 6.2 未來展望 121 參考文獻 122 附錄A-橢圓軌跡圖 124 附錄B-勁度瑕疵之影響 129 | |
dc.language.iso | zh-TW | |
dc.title | 諧振半球殼之質量瑕疵分析與修正 | zh_TW |
dc.title | Analysis and Correction of Mass Imperfection of a Hemispherical Resonant Shell | en |
dc.type | Thesis | |
dc.date.schoolyear | 103-2 | |
dc.description.degree | 碩士 | |
dc.contributor.coadvisor | 謝發華 | |
dc.contributor.oralexamcommittee | 張簡文添,周傳心,陳柏智 | |
dc.subject.keyword | 半圓球殼,漢彌頓原理,自然頻率,特徵向量,橢圓軌跡圖, | zh_TW |
dc.subject.keyword | Hemispherical shell,Hamilton principle,natural frequency,bifurcate frequency,eigenvectors, | en |
dc.relation.page | 131 | |
dc.rights.note | 未授權 | |
dc.date.accepted | 2015-08-14 | |
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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