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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/19896
標題: | 諧振半球殼參數設計與質量瑕疵數值模擬 Parametric Analysis of a Hemispherical Resonant Shell and Numerical Simulation of Mass Imperfection |
作者: | Ming-Zong Weng 翁銘宗 |
指導教授: | 張家歐(Chia-Ou Chang) |
關鍵字: | 半圓球殼,陀螺儀,數值模擬,瑕疵,修正, hemispherical shell,HRG,imperfection,trim, |
出版年 : | 2015 |
學位: | 碩士 |
摘要: | 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。 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. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/19896 |
全文授權: | 未授權 |
顯示於系所單位: | 應用力學研究所 |
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