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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 張家歐(Chia-Ou Chang) | |
| dc.contributor.author | Ming-Zong Weng | en |
| dc.contributor.author | 翁銘宗 | zh_TW |
| dc.date.accessioned | 2021-06-08T02:25:44Z | - |
| dc.date.copyright | 2015-08-28 | |
| dc.date.issued | 2015 | |
| dc.date.submitted | 2015-08-18 | |
| dc.identifier.citation | [1] David M. Rozell, 2009, 'The Hemispherical Resonator Gyro: From Wineglass to the Planets,' Proc. 19th AAS/AIAA Space Flight Mechanics Meeting, pp.1157-1178. [2] A.D. Meyer and D.M. Rozelle, 2012, “Milli-HRG inertial navigation system,” Position Location and Navigation Symposium (PLANS), IEEE/ION, 23-26 April 2012, pp.24-29. [3] Rayleigh, L, 1881, “On the Infinitesimal Bending of Surfaces of Revolution,” Proc. Math. Soc., London, Vol.13, pp. 4-16. [4] Love, A. E. H., 1888, “On th Small Free Vibrations and Deformation on Thin Elastic Shells,” Phil. Transactions Roy. Soc., A179, pp. 491-546. [5] Washizu, K., 1980, Variational Methods in Elasticity and Plasticit, Pergamon Press Ltd., 3rd. [6] Niordson, F. I., 1985, Shell Theory, North Holland, Amsterdam. [7] 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. [8] Quick, W. H, 1964, “Theory of the Vibrating String as an Angular Motion Sensor,” Transactions ASME, J. Appl. Mech., pp. 523-534 [9] 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 [10] 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. [11] Chou, C. S., Chang, C. O., and Huang, J. J., 1996, “The Vibration of a Rotating Hemispherical Shell Excited by Electrostatic Field,” International Journal of Applied Electromagnetics in Materials, Vol. 7, No. 2, pp. 21-42. [12] Chou, C. S., and Chang, C. O., 1997, “Modal Precession of a Hemispherical Shell Gyro Excited by Electrostatic Field,” Japanese Journal of Applied Physics, Vol. 36, No. 11, pp. 7073- 7081. [13] Chou, C. S., Chang, C. O., and Huang, J. J., 1999, “Vibration of a Hemispherical Shell Gyro Excited by an Electrostatic Field,” International Journal of Applied Electromagnetics in Materials, Vol. 10, No. 4, pp. 425-49. [14] 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。 [15] 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。 [16] 謝發華，2013，殼振動陀螺儀原理分析，中山科學研究院。 [17] 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。 [18] 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。 [19] 林思嘉，2015，瑕疵諧振半球殼之頻率分析與修正，碩士論文，台灣大學應用力學研究所。 [20] Jae Yoong Cho; Najafi, K., 2015, “A high-q all-fused silica solid-stem wineglass hemispherical resonator formed using micro blow torching and welding, ” Micro Electro Mechanical Systems (MEMS), pp.821,824, 18-22 Jan. [21] Qian Yang; Guoxing Yi; Bochang Shen; Henian Wang, 2006, 'Kinetic model analysis and testing of HRG,' Systems and Control in Aerospace and Astronautics, ., pp.5 pp.,109 [22] Shengli Gao; Jiantong Wu, 2007, 'Theory and Finite Element Analysis of HRG,' International Conference on Mechatronics and Automation, pp.2768,2772. [23] CORNING, “Corning® HPFS® 7979, 7980, 8655 Fused Silica” | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/19896 | - |
| dc.description.abstract | Niordson的半圓薄球殼理論的正解只適用於沒有瑕疵的半圓球殼，且不能完整地描述半圓球殼陀螺儀，因陀螺儀的半圓薄殼的極點固定於支撐柱上，故本研究使用商用軟體的有限元素法(FEM)對支撐柱半圓球殼進行模擬分析。球殼受外部電場激發特定模態而自由振動，使用FEM分析含支撐柱半圓球殼各個共振模態與其自然頻率的值，選擇合宜的支撐柱尺寸範圍，將其他的共振模態的自然頻率遠離驅動模態的自然頻率；並且比較含支撐柱之半圓球殼與無支撐柱之半圓球殼的差異，以及比較FEM數值解與Lord Rayleigh近似解析解的差異。質量瑕疵造成頻率的分岐與共振模態方向的改變可由FEM模擬計算求得，透過對低頻的反節點以雷射去質量方式來消除自然頻率的分岐。 | zh_TW |
| dc.description.abstract | The exact solution of hemispherical thin shell obtained by Niordson is applicable for shell without imperfection. Also his solution is inapplicable for hemispherical resonator gyroscope (HRG), because the hemispherical shell of HRG has its pole fixed on a supporting post. The finite element method (FEM) of the commercial code COMSOL is used to analyze the vibration of the hemispherical shell (HS). The shell is excited into vibration by applying electrical field. The vibration modes and the corresponding natural frequencies are numerically simulated through FEM. The comparisons between the HS without supporting post and that with supporting post are studied. Also the difference between the FEM solutions and the approximate solution obtained by Lord Rayleigh is analyzed. The effect of mass imperfection on the frequency bifurcation and the orientation change of the resonant modes are investigated. Different types of imperfection are considered such as mass addition or removal along the latitudinal or azimuth direction. The bifurcated frequencies and the offset vibration modes caused by the imperfection can be calculated through FEM. The two bifurcated frequencies can be made equal by removing the mass at the antinode point of the lower-frequency resonant mode by laser trimming. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T02:25:44Z (GMT). No. of bitstreams: 1 ntu-104-R02543024-1.pdf: 12744415 bytes, checksum: b9bc50fb3664353d93c978a088260084 (MD5) Previous issue date: 2015 | en |
| dc.description.tableofcontents | 誌謝 i 中文摘要 ii ABSTRACT iii 目錄 iv 表目錄 vii 圖目錄 ix 第1章 緒論 1 1.1 前言 1 1.2 研究目的 2 1.3 文獻回顧 3 1.4 論文架構 4 第2章 Niordson線性薄殼理論[15][16] 5 2.1 抗變向量與協變向量 5 2.2 座標系統 6 2.2.1 二維曲面座標系統 6 2.2.2 三維簡正座標系統 8 2.3 Niordson薄殼基本理論 9 2.3.1 應變量與位移 10 2.3.2 虎克定律與應變能 11 2.3.3 薄膜應力張量與彎矩張量 13 第3章 半圓球殼振動陀螺儀運動方程式[15][16] 15 3.1 漢彌頓原理(Hamiltion’s principle) 15 3.1.1 半圓球殼之旋轉動能 15 3.1.2 二維曲面座標系統中的旋轉動能 17 3.1.3 半圓球殼之應變能 19 3.1.4 外部負載 22 3.2 漢彌頓原理 24 球座標 24 3.2.1 變分原理與邊界條件 30 3.3 半圓球殼之運動方程式 31 3.3.1 雷利近似解特徵模態展開法 31 3.3.2 感測係數 36 3.3.3 勁度係數 40 3.3.4 感測方程式 42 3.4 缺陷半圓球殼振動陀螺儀 45 第4章 支撐柱的半球殼之數值模擬與設計 48 4.1 數值模擬的設定 48 4.1.1 半圓球殼的幾何參數與材料參數 48 4.1.2 半圓球殼的模態命名 49 4.1.3 收斂性分析 54 4.2 比較球殼近似解與數值模擬的自然頻率 55 4.3 半圓球殼陀螺儀之尺寸與模態的關係 58 4.3.1 支撐柱高的設計 58 4.3.2 支撐柱半徑與夾持高度的設計 61 4.3.3 以曲線擬合建立自然頻率的比值 66 4.3.4 等比例放大半球殼的尺寸 72 4.4 設計總結與建議 74 第5章 瑕疵半圓球殼之數值模擬分析 75 5.1 半圓球殼之瑕疵模型 76 5.1.1 方向密度的瑕疵 76 5.1.2 方向密度之瑕疵 80 5.2 瑕疵模型之修正 82 5.2.1 方向密度瑕疵之修正 83 5.2.2 方向與 方向密度的瑕疵 87 5.2.3 雙瑕疵模型之修正 91 5.2.4 三瑕疵模型之修正 93 5.3 挖洞修正瑕疵的模型 95 第6章 結論 98 參考文獻 99 附錄A 101 附錄B 113 | |
| dc.language.iso | zh-TW | |
| dc.title | 諧振半球殼參數設計與質量瑕疵數值模擬 | zh_TW |
| dc.title | Parametric Analysis of a Hemispherical Resonant Shell and Numerical Simulation of Mass Imperfection | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 103-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.coadvisor | 張簡文添(Wen-Tien Chang-Chien) | |
| dc.contributor.oralexamcommittee | 謝發華,周傳心,陳柏志 | |
| dc.subject.keyword | 半圓球殼,陀螺儀,數值模擬,瑕疵,修正, | zh_TW |
| dc.subject.keyword | hemispherical shell,HRG,imperfection,trim, | en |
| dc.relation.page | 117 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2015-08-18 | |
| 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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