微結構系統的動態行為受到靜電場耦合效應、殘留應力、拉伸應力、壓膜阻尼(squeeze damping)及雜散電場效應的影響，是一相當複雜之問題。本文應用微分轉換混合有限差分法探討受靜電驅動之微結構系統的動態特性研究。
一開始介紹微分轉換理論的基本定義、性質與公式的推導及演算的方法，然後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，藉由轉換得到之迭代方程式進行代數運算求取微結構之撓度及吸附電壓值。並利用混合微文轉換與有限差分法探討微橋狀樑在靜電驅動下，殘留應力及壓膜阻尼(squeeze damping)效應對於吸附電壓的影響。然後探討在直流與交流驅動電壓結合下，微橋狀樑受靜電驅動的動態行為。接著同樣應用混合微分轉換法與有現差分法擴展到二維的微結構(微平板)的吸附電壓研究。最後，探討在結合直流與交流驅動電壓下微平板的動態行為。
研究結果中發現，壓膜阻尼(squeeze damping)效應對於均勻電場靜電力驅動之微橋狀樑的吸附電壓影響甚微，相較之下殘留應力對於微橋狀樑之吸附電壓的影響要大得多。以混合微分轉換法與有限差分法求取二維微平板之吸附電壓與文獻之實驗測量值互相比較，誤差在2%以內，可以說是相當準確。混合微分轉換法與有現差分法是一簡單容易理解、具系統性的分析方法對於求一維或多維度之非線性偏微分方程來說。

The dynamic behavior of microsystems devices is problematic due to the complexity of the interactions between the electrostatic coupling effect, the residual stress, the tensile stress, the squeeze damping effect, the fringing field effect, and the nonlinear electrostatic force. In this study, we apply the hybrid differential transformation and finite difference method on the dynamic analysis of nonlinear electrostatic-actuating microsystems.
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 displacement and the pull-in voltage of the micro fixed-fixed beam can be obtained. And we discuss the residual stress and squeeze damping effect to the pull-in voltage of electrostatic-actuating micro fixed-fixed beam by the hybrid differential transformation and finite difference method. Second, this study proposes the actuation method that combines DC and AC loading and analyzes the dynamic response of the micro fixed-fixed beam. Third, applying the differential transformation and finite difference method on the analysis of pull-in voltage of micro plate. Finally, this study proposes the actuation method that combines DC and AC loading and analyzes the dynamic response of the micro plate.
The results of this study show that the squeeze damping effect has no significantly effect for the pull-in voltage of an electrostatically actuated micro fixed-fixed beam, and the residual stress has significantly effect. Applying hybrid scheme to solve the pull-in voltage of micro plate is precise which the deviation is no more than 2% from the experimental results obtained by literature. The hybrid differential transformation and finite difference method presents a simple and more systematic procedure in solving the one-dimensional or multidimensional linear and nonlinear equation than other analyses.

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