本論文主要探討在微機電系統中之空氣薄膜擠壓效應對靜電式雙鉗微共振樑的影響。由於靜電力能量密度太小，一般利用靜電驅動方法所設計之微共振器，動輒需要數十伏特的高電壓方能驅動結構共振。而最有效降低驅動電壓的方法，即為縮小電極與微共振樑間的距離。但空氣介質在狹小間隙中所產生的擠壓薄膜效應，將使得空氣性質隨著系統驅動頻率及不同的環境壓力下，出現類似阻尼特性的模式，而這也將改變微共振器系統的動態行為。
文中先以Lagrange’s equation建構雙鉗共振樑之運動方程式，並利用假設模態法求解自然頻率問題。並藉由能量轉換模式來描述兩相近物體間的空氣薄膜擠壓效應，在黏滯阻尼模式假設下，得到一擁有尺寸、環境溫度與壓力等參數之阻尼因子。最後由分析系統頻率響應函數，得到微共振樑之阻尼比等動態特性。除此之外，文中亦探討微共振樑受到軸向負載時，對微共振器輸出頻率產生的變化。

This paper is going to emphasize on the air squeeze film damping effect on micro-mechanical resonant beam in MEMS. In general, the low energy density of electrode force will cause high-voltage power supply to drive the electro- micro resonators; reducing the distance between the electrode and resonant beam can be the most efficient way to solve this problem. But bringing different exciting frequency of system and environmental pressure to the air squeeze film effect might cause it changes form similarly to the damping qualities, and this will also change the dynamic characteristics of micro resonator.
The dynamic model for double clamped micro-mechanical resonant beam is proposed by using Lagrange’s equation in this study. The corresponding eigenvalue problems of resonant beam are formulated and solved by employing the hypothetical mode method. Under the presumption of viscous damping model, we may obtain a damping factor which includes the parameters of size, temperature and air pressure when energy transfer model is employed to simulate the squeeze film damping effect of two immediate objects. Eventually, the damping ratio and the dynamic characteristics of resonant microbeam are derived by means of exploring the frequency response function of system. Besides, the frequency change of micro-mechanical resonant beam due to an axial force is also considered in the thesis.

目錄 I
圖目錄 IV
表目錄 VIII
符號說明 IX
摘要 XV
Abstract XVI
第一章 緒論 1
1-1 前言 1
1-1-1 簡介 1
1-1-2 研究背景與動機 10
1-1-3研究方法與目標 13
1-2文獻回顧 15
1-2-1 微共振器 15
1-2-2 微結構之空氣阻尼效應 16
1-2-3 假設模態法 17
1-3 組織與章節 18
第二章 能量轉換模式 20
2-1自由氣體分子 20
2-2 能量轉換模式[23] 23
2-2-1能量轉換模式之主要假設 23
2-2-2 撞擊後氣體分子速度 25
2-3 低真空下氣體薄膜擠壓效應 28
2-4 阻尼因子 35
第三章 微共振樑運動方程式導引 39
3-1 雙鉗微共振樑運動方程式之推導 39
3-2 模態分析 47
第四章 空氣薄膜阻尼參數分析 52
4-1 微共振樑自然頻率 52
4-2 空氣薄膜擠壓阻尼因子 54
4-2-1 間隙距離 54
4-2-2 真空狀態 64
4-2-3 溫度效應 67
4-2-3 微共振樑尺寸效應 70
第五章 結論 78
5-1 結論 78
5-2 未來展望 80
參考文獻 81
Appendix A 85

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