本文應用混合微分轉換/有限差分法探討非線性結構與靜電力、靜水壓力、殘留應力、黏滯力及熱應力效應的影響下，非線性結構系統的動態研究。首先介紹微分轉換法理論的定義及計算方法，接著應用微分轉換法將圓板之統御方程式轉換成迭代方程式，透過頻率方程式計算得到圓板的自然頻率與振動模態並探討微分轉換階數及非局域參數對自然頻率的影響。接下來將微分轉換法結合有限差分法針對非局域彈性理論、表面彈性理論、修正耦合應力理論在靜電驅動及靜水壓力效應下進行數值模擬並探討不同參數對奈米圓板吸附現象之影響。進行數值建模時使用微分轉換法處理時間域後再以有限差分法處理空間域並以數值軟體進行迭代計算。先以受靜電力及靜水壓力影響下探討非局域性彈性奈米圓板之行為。接下來混合直流電及交流電情況下探討表面彈性理論奈米圓板之動態行為。最後，探討修正耦合理論奈米圓板受靜水壓力及靜電力影響下之行為。研究結果得知非局域參數、表面參數、材料長度參數皆會顯著的影響圓板致動器之吸附值。
混合微分轉換/有限差分法與不同文獻之數值模型與實驗比較結果相當準確，誤差皆在7.4%以內，因此確認混合微分轉換/有限差分法是一種簡單並能有效應用於複雜非線性數值問題的數值方法。

關鍵字:奈米機電系統、微分轉換法、非局域彈性理論、表面彈性理論、修正耦合應力理論、吸附電壓

In recent years, the electromechanical systems problems is popular form the consideration of microscale to nanoscale. Some physical effects negligible on microscale have appreciable consequences at nanoscale. The classical theory cannot model and analyze the nanoscale problems accurately. The hybrid differential transformation / finite difference method is used to analyze various non-classical models. The hybrid method is used to model the governing equation problems of nonlocal elasticity theory, surface elasticity theory and modified couple stress theory (MCST). The electrostatically actuators are affected by various material and physical parameters, and the effects of physical effects and theories on the actuators are discussed. The effects of physical parameters on the actuators is discussed. The numerical results show that the nonlocal parameters, surface parameters and material length parameters all affect the pull-in values. The differential transformation method is simpler than other methods on complex nonlinear problems.
Keywords: Nanoelectromechanical system, Differential transformation method, Nonlocal elasticity theory, Surface elasticity theory, modified couple stress theory, Pull-in voltage

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