本文應用微分轉換結合有限差分法探討在微結構系統與靜電場耦合效應、殘留應力及雜散電場效應的複雜影響下，受靜電驅動之微結構系統的動態特性研究。
首先介紹微分轉換理論的基本定義、性質及推導演算方法，接著應用微分轉換法將微橋狀樑之統御方程式轉換成迭代方程，藉由符號運算及在頻率方程式上做簡單代數計算，可以得到微橋狀樑的自然頻率；其次，說明殘留應力及雜散電場效應對微結構系統的影響，並利用混合微文轉換與有限差分法(混合法)求解微結構樑在靜電驅動下受殘留應力及雜散電場效應影響的吸附電壓。同時，亦應用混合法分析在殘留應力與流體靜壓力效應影響下，受靜電驅動之微泵膜片的暫態行為；最後，探討在直流與交流驅動電壓結合下，受靜電驅動之微橋狀樑的動態行為。
研究結果顯示使用混合法所求解的吸附電壓與文獻中的實驗值或其他數值相互比較，其誤差皆在2%內，堪稱非常精確。因此，混合微分轉換與有限差分法是一個比其他分析方法更簡單、更具系統性來求解非線性偏微分方程式的有力工具。

This study, the hybrid differential transformation and finite difference method, is employed to analyze the dynamic behavior of an electrostatically actuated micro-structure system under the complexity influence of the interactions between the electrostatic coupling effect, the residual stress and the fringing field effect.
First, the basic definitions, properties and calculation are introduced. The governing equation of the micro fixed-fixed beam is solved using the differential transformation to become an algebraic equation that is suitable for symbolic computation. Then, the natural frequency of the micro fixed-fixed beam can be obtained. Second, applying the differential transformation and finite difference method (hybrid method) solve the governing equation of an electrostatically actuated micro system to obtain the pull-in voltage and the effect of fringing field to micro system is mentioned. The hybrid scheme is employed to analyze the pull-in phenomenon of an electrostatically actuated micro circular plate system which explicit account is taken of both the hydrostatic pressure and the residual stress. Finally, this study proposes the actuation method that combines DC and AC loading and analyzes the dynamic response of the micro fixed-fixed beam.
The results of this study show that applying hybrid scheme to solve the pull-in voltage is precise which the deviation is no more than 2% from those derived in the literature using a variety of different schemes. Overall, the hybrid differential transformation and finite difference method presents a simple and more systematic procedure in solving the linear and nonlinear equation than other analyses.

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