本文主要在推導具錘型端點微致動器之基本頻率分佈與模態形式。期能建立其相關形狀與尺寸參數對此基本動態特性之關聯性。文中利用Hamilton原理配合樑理論及特殊之錘型端點邊界條件，建立基本運動方程式。研究中亦利用Adomian decomposition method 探討了各設計參數對此型致動器在不同電場條件下之靜態變形與無阻尼假設下之端點動態響應。文中亦利用ANSYS有限元素套裝軟體對所建模式之正確性進行量化驗證，分析結果顯示所推導建立之微致動器數學公式，可精確預估不同設計參數下之靜動態響應。
相關數值結果顯示，適宜之錘型微致動器參數設計，可有效控制在不同靜電場操作下之靜動態響應。有限元素結果亦驗證了此建立運動方程之適用性。希此研究結果將有助於未來此型微致動器之開發與設計工作。

The dynamic equations of micro-hammer-type actuators are derived by employing Hamilton’s principle with the specific boundary conditions. The effect of shape and size parameters on the distribution of natural frequencies and mode shapes has also been evaluated and investigated in this study. The effect of lump mass of the end hammer on the dynamic behavior of this type actuator was studied.
The Adomian decomposition method was used to derive the deformation of the actuator with different static electric field intensity. The deformations solved from ANSYS Finite Element Software have been checked to testify the accuracy of the results calculated from the proposed model. Numerical results indicate that the proposed model and the derived equation are feasible to simulate the static and dynamic responses of this type hammer actuator with acceptable accuracy. It is expected that the proposed equations of motion are helpful to the designers to explore the relation between the design parameters and the performance of the micro-hammer-type actuators in the near future.

謝誌 i
摘要 ii
Abstract iii
目錄 iv
表目錄 vi
圖目錄 vii
符號說明 ix
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.3 研究動機與組織章節 6
第二章 錘型微致動器之理論推導 8
2.1 錘型微致動器受靜電力驅動之之能量式 8
2.1.1 平行板電容原理 8
2.1.2 靜電力驅動下之能量式 9
2.2錘型微致動器之靜態解 13
2.2.1 Hamilton's principle介紹 13
2.2.2 Hamilton's principle之推導 14
2.2.3 特徵值問題求解系統模態 21
2.2.4 利用Adomian Decomposition Method解決初始值問題 23
2.3錘型微致動器之動態分析 26
2.3.1 錘型微致動器之模態正交性 26
2.3.2 錘型微致動器之動態行為 29
第三章 錘型微致動器之自然頻率與模態探討 32
3.1 有限元素模型 32
3.1.1 建立有限元素模型及參數設定 32
3.1.2 斂散性分析 36
3.2 錘型微致動器之模態 38
3.3 改變錘型微致動器樑端參數之自然頻率影響 41
3.4 改變錘型微致動器前方錘型質量塊大小之自然頻率影響 43
第四章 錘型微致動器之靜態與動態行為 46
4.1 改變作用電壓之位移影響 46
4.2 錘型微致動器之根部應力探討 51
4.3 錘型微致動器之自由振動 53
第五章 結論與未來工作 56
5.1 結論 56
5.2 未來工作 57
參考文獻 58

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