本篇論文主要是利用解析方法與數值分析分別探討在側向振動梳狀微結構裡的流場模型，在解析解方面主要以Stokes type flow模型來估算阻尼值，並且考慮加入滑動邊界的情況對此系統所造成的影響。另一方面以數值的方法來模擬梳狀微結構裡的流場，我們利用有限差分法來離散非穩態不可壓縮Navier-Stokes方程式，直接求解其二維、非穩態、不可壓縮、黏性流之速度場，且分別比較不可滑動及滑動邊界條件對此系統所造成的影響，並探討在微小梳狀加速度器內的流體情況，且模擬計算出各物理量，並且探討梳狀微結構的尺寸、頻率在此系統中之重要性，以得到空氣黏滯效應，並進一步求得品質因子與阻尼之值，並以解析解、數值解與前人的實驗結果加以比對。我們的解析解所得之結果與前人實驗結果相比，其估算之品質因子不論滑動邊界或是不可滑動邊界條件其值均稍大於實驗值，造成誤差的原因為我們把實際的三維流場簡化成二維流場，且忽略了振動質量邊界對流場所造成的影響。另外以數值法所模擬計算的品質因子與實驗值相當接近，但數值方法計算所需時間相當長，未來仍舊有改良的空間。

This paper studies analytically as well as numerically viscous air damping in laterally oscillating micro comb structures. The influences of dimension and frequency on viscous damping are investigated. The Knudsen numbers in typical micro comb structures indicate part of the flow falling in the slip flow region. The slip effect is also studied. The analytical results demonstrate that the transient motion is damped out in less than one oscillating period of the model system. The analytical quality factors subject to slip and nonslip boundary conditions are both larger than experimental data. The numerical procedure solves the unsteady two-dimensional incompressible Navier-Stokes equations. The Marker-And-Cell (MAC) finite difference method and a Poisson equation solver are used to solve the equations. The numerical quality factors compare quite well with experimental data. The possible explanation for the discrepancy between analytical and numerical results are that analytical solutions assume the structure is infinite in the lateral direction, while numerical solutions treat the structure as finite, the edge and finite-size effects are included.

中文摘要……………………………………………………………………………i
英文摘要………………………………………………………………………… ii
目錄………………………………………………………………………………iii
符號說明……………………………………………………………………………v
圖表說明…………………………………………………………………………vii
一 緒論……………………………………………………………………………1
1-1研究目的……………………………………………………………………1
1-2微加速度計簡介 …………………………………………………………2
1-3研究方法……………………………………………………………………3
二 解析解…………………………………………………………………………5
2-1梳狀結構流場………………………………………………………………5
2-2統御方程式…………………………………………………………………6
2-3邊界條件……………………………………………………………………8
2-4各區之解析解………………………………………………………………9
三 數值分析………………………………………………………………………18
3-1交錯網格…………………………………………………………………18
3-2統御方程式………………………………………………………………18
3-3統御方程式的離散化……………………………………………………19
3-4邊界條件…………………………………………………………………23
3-5求解步驟…………………………………………………………………25
四 結果與討論……………………………………………………………………27
五 結論與建議……………………………………………………………………31
5-1結論………………………………………………………………………31
5-2建議………………………………………………………………………32

[1] M. Madou, Fundamantals of Microfabrication, CRC Press, (1997).
[2] R.M. Langdon, “Resonator sensors — a review,” J. Phys. E: Sci. Instrum., vol.18 pp.103-115, (1985).
[3] X. Zhang and W.C. Tang, “Viscous Air Damping in Laterally Driven Microresonators,” Proc. IEEE Workshop on Microelectromechanical Systems, pp.199-204, (1994).
[4] W.S. Griffin, et al., “A study of fluid squeeze-film damping”, Journal of Basic Engeering, Transaction of ASME, June,, pp.452-456, (1966).
[5] Y.H. Cho, B.M. Kwak, A.P. Pisano and R.T. Howe, ”Viscous Energy Dissipation in Laterally Oscillating Planar Microstructures: A Theoretical and Experimental Study,” Proc. IEEE Workshop on Microelectromechanical Systems, pp.93-98, (1993).
[6] 楊龍杰,李其源,張培仁, “半導體微型加速度計梳狀結構之流場阻尼分析”, 國科會研究報告,計畫編號NSC87-2218-E-002-015.
[7] 楊龍杰, 半導體微型加速度計及其相關技術之研究, 國立台灣大學應用力學研究所博士論文, 中華民國八十六年元月.
[8] H. S. Carslaw and J. C. Jaeger, Conduction of heat in solids, Clarendon Press, Oxford, (1959).
[9] M.Necati Ozisik, Heat conduction, Wiley, New York, (1980).
[10] E.A. James, Gas Dynamics, 2nd Edition, Allyn and Bacon, Boston, (1933).
[11] Robert W. Fox and Alan T. McDonald, Introduction to Fluid Mechanics, 4th Edition, John Wiley & Sons, Inc., New York, pp.306-310, (1994).