研究生: |
林峰安 Feng-an Lin |
---|---|
論文名稱: |
壓電式振動陀螺儀之三維有限元素分析 3-D Finite Element Analysis of a Piezoelectric Vibrator Gyroscope |
指導教授: |
廖崇禮
Chung-Li Liao |
口試委員: |
呂森林
Sen-Lin Lu 蔡哲雄 Jhe-syong Cai |
學位類別: |
碩士 Master |
系所名稱: |
工程學院 - 機械工程系 Department of Mechanical Engineering |
論文出版年: | 2009 |
畢業學年度: | 98 |
語文別: | 中文 |
論文頁數: | 95 |
中文關鍵詞: | 振動陀螺儀 、三維 、有限元素 |
外文關鍵詞: | Finite element, Vibrator gyroscope, Three-dimensional |
相關次數: | 點閱:213 下載:1 |
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本文主旨為建立三維有限元素分析模式以分析壓電迴轉平板之動態特性,並探討迴轉角速度的大小與方向對壓電平板之自然頻率、模態與輸出電壓的影響。
本文首先推導壓電迴轉平板內任一點之速度與加速度方程式,接著使用漢米爾頓原理(Hamilton’s principle)與有限元素之近似解、加速度場與壓電材料本構方程式,推導出壓電式振動陀螺儀(piezoelectric vibrator gyroscopes)之有限元素運動方程式,由此有限元素運動方程式並利用求取保守迴轉體系統(conservative gyroscopic system)之特徵值與特徵向量的方法,可求得本文壓電迴轉平板之自然頻率與模態。分析結果並與文獻作比較,以驗證本文分析模式的準確性。
本文另探討壓電方形板之旋轉角速度大小與其偏轉角對其自然頻率與模態的影響,最後亦探討旋轉角速度大小與其偏轉角對壓電方形板輸出電壓之影響。
The objective of the present study is developing a 3-D finite element analysis model to analyze the dynamic characteristics of rotating piezoelectric plates. The effect of rotating velocity on the natural frequencies, modes and output voltage is also investigated.
First, this study derives the equations of velocity and acceleration of any point in the rotating plate. Then this study uses the Hamilton’s principle and the finite element approximate solution to derive the finite element equation of motion for the present rotating piezoelectric plate. Finally, applying the method for computing the eigenvalues and eigenvectors of conservation gyroscopic system and the present finite element model this study find the natural frequencies and vibration modes of the rotating piezoelectric plate. The present results are compared with that in the literature to verify the accuracy of this finite element model.
From the numerical examples, the effects of magnitude and direction of rotating speed on the natural frequencies, the vibration shapes, and the output voltages are investigated to demonstrate the sensing capability against the rotating speed.
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