臺灣博碩士論文加值系統

摘 要
本論文將探討線性與非線性的偏光鏡動態行為，此偏光鏡是由兩層壓電陶瓷中間夾著黃銅且兩邊固定，中間放一層薄薄的鏡子。描述動態行為的非線性的統御方程式可以由漢彌頓原理推導出來，並由此可觀察出偏光鏡受到電壓和分段電極的影響，就像是有受到外加的純力矩作用。有限元素法被應用於一個均勻樑受到同等外加純力矩作用下和此偏光鏡的動態行為作一比較，並且驗證了本文中的理論是正確有效的。為了得到最大的偏轉角度，對分段電極和厚度的比例作最佳化設計，可以求出最佳的比例長度。對鏡子和總長度的比例作靈敏度分析，取第二個模態特徵值來分析和預測，可以預測一個極為精準的特徵值。最後，對於有關非線性的動態模擬、最佳化設計和靈敏度分析，應用一個簡化的方式來節省電腦運算時間和簡化繁雜的數學式子。

ABSTRACT
This paper studies the linear and nonlinear dynamic behavior of the optical beam deflector, which is composed of two piezoelectric layers and one sandwiched brass layer with both ends clamped. The nonlinear equation describing the dynamic behavior is derived by Hamilton''s principle. An equivalent configuration of the optical beam deflector with external moments is obtained to analyze the effect of the applied voltage and split electrodes. The finite element method is employed to compare the dynamic responses with a uniform beam and to validate the theoretic analysis. The nonlinear optimization problems with respect to the electrode length ratio and thickness ratio are solved for the maximum deviation angle. The sensitivity of the second mode eigenvalue with respect to the length ratio of the mirror part to total length is performed. A simplified method for the dynamic response, optimal design and sensitivity analysis of the nonlinear system is proposed to save the computation time and avoid the complicated mathematics.

Contents
摘 要...................................................................I
Abstract.................................................................II
誌 謝..................................................................III
Contents................................................................IV
計畫緣由與目的................................................VI
研究方法與成果...............................................VII
討論與結論.......................................................VIII
Figure Caption......................................................IX
Table Caption.........................................................X
Nomenclature........................................................XI
1. Introduction.........................................................1
2. Dynamic Model Development............................3
2-1 Physical Model...............................................3
2-2 Equations of Motion ......................................3
2-2-1 Nonlinear Equations of Motion................3
2-2-1-1 Independent variables , and D...........4
2-2-1-2 Independent variables , and. .............8
2-2-1-3 Compare the two results....................9
2-2-2 Uniform Beam of Motion.......................10
3. Finite Element Formulation...............................12
4. Optimal Design.................................................15
5. Sensitivity Analysis...........................................17
5-1 Design Sensitivity.........................................17
5-2 Eigenvalue Sensitivity...................................18
6. Numerical Results.............................................20
6-1 Optimal Design.............................................20
6-2 Design Sensitivity Analysis...........................21
6-3 Eigenvalue Sensitivity....................................23
7. Conclusion.........................................................23
Acknowlegment.....................................................24
Reference................................................................24
Figure.....................................................................27
Table.......................................................................33
簡 歷....................................................................36

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