臺灣博碩士論文加值系統

隨著半導體製程技術快速的成長，微/奈米機電系統發展相對成熟，在微小精密電子電路訊號處理的要求下，微致動器之應用需求也相對提升，其中又以靜電驅動微致動器最為廣泛。因傳統半導體元件體積大又重，加上其消耗功率高，無法達到目前所需之要求。為了解決傳統元件之問題，故應用微/奈米機電技術，達到功能整合、頻寬大、訊號損失低和體積小等要求。由於石墨烯的低質量密度以及高強度，且它的化學和機械之穩定性佳，適合於微/奈米元件在高速、高敏感、高電流密度之應用。
本旨在提出靜電驅動微致動器電極之系統性分析與設計方法，並以單層石墨烯薄板為基本元件進行探討。由於無網格法具有無網格依賴性、前處理只需要節點位置信息，容易分析等優點，因此本文採用無網格伽遼金法(Element free Galerkin method；EFGM)進行分析，首先利用漢米爾頓(Hamilton)原理推導橫向振動方程，由移動最小二乘法(Moving least square；MLS)之形狀函數離散，再透過背景網格數值化，最後利用特徵值問題(Eigenvalue Problem；EVP)探討其動態特性，接著引入非局域性彈性理論和在靜電驅動下之單層石墨烯薄板其吸附現象分析。
為了展現本研究所提出之優化設計方法、步驟與流程之可行性，所以透過三個實用範例，探討本文方法之優勢。首先以一塊金屬平板做為第一範例顯示本文方法之精度，誤差皆在2%內。應用非局域性彈性理論為第二範例，探討單層石墨烯薄板在無外力做用下之動態分析。最後以施加靜電力為第三範例，觀察靜電驅動下之單層石墨烯之結構變化。經由三種範例模擬結果顯示，透過非局域參數和靜電驅動對結構在動態分析皆有頻率降低之現象。而由無網格伽遼金法(EFGM)分析下，發現此法快速地提供吸附現象所需之吸附電壓做為一個參考價值及為降低實驗成本所需之研究方法。

With the rapid growth of semiconductor process technologies, micro / nano-electromechanical systems is well developed. Nowadays, the conventional semiconductor device can’t meet the requirements because of its weight, bulk and high power consumption. The application of micro / nano electromechanical technology to achieve functional integration, bandwidth, low signal loss and small size requirements is used to solve this problem. Graphene have excellent chemical and machinery stability and it’s suitable for the application of micro / nano components in high speed, high sensitivity and high current density.

This paper shows systematic analysis and design methods for actuator electrodes of electrostatic driving micro actuator, and further discuss about the graphene sheet as the basic element. Meshfree method with no grid dependence, it is only necessary to know the information of node location. It is easy to analyze the data. Thus, we adopted EFGM as our methods. Finally apply an electrostatic force and nonlocal elastically theory to observe the changes in the structure of the graphene.

Simulation results show that: through the nonlocal parameters and electrostatic driving will cause reduction of frequency in the structure. By the EFGM analysis, it can be observed that method provides not only the value of voltage rapidly which arise adsorption phenomena but also reduces the cost of experiments. The value could be as a reference to company.

中文摘要 I
Extend Abstract III
誌謝 VI
目錄 VII
表目錄 X
圖目錄 XI
符號目錄 XIV
第一章 緒論 1
1.1 研究動機 1
1.2 研究目的 3
1.3 章節瀏覽 4
第二章 文獻回顧 5
2.1 應用回顧 5
2.1.1 石墨烯基本特性應用回顧 5
2.1.2 微致動器系統之吸附作用回顧 6
2.1.3 無網格在固體力學上應用回顧 9
2.2 理論回顧 12
2.2.1 靜電驅動微致動器之理論 12
2.2.1(a) 平行板電容之原理 13
2.2.2 非局域性彈性理論之回顧 15
2.2.3 無網格伽遼金之方法與步驟 18
2.2.3(a) 全域伽遼金弱形式 19
2.2.3(b) 漢米爾頓(Hamilton)原理20
2.2.3(c) 支持域與影響域 21
2.2.3(d) 形狀函數(shape function) 23
2.2.3(e) 加權函數(weight function) 26
2.2.3(f) 本質邊界條件處理 28
2.3 無網格法之積分處理 29
2.4 無網格之優缺點 31
第三章 無網格伽遼金法模擬平面薄板之理論模型建構 45
3.1 平面薄板物理模型之基本假設 45
3.2 薄板動態分析之勢能函數選擇 45
3.3 無網格動態特徵分析流程 49
3.3.1 移動最小二乘法(MLS) 近似場函數 49
3.3.2 薄板動態模型之離散處理 50
3.3.3 背景網格數化求得場方程 52
3.4 無網格分析動態薄板之程式步驟流程 54
第四章 石墨烯薄板致動模擬印證及應用例 57
4.1 以薄板自由振動做理論驗證 57
4.1.1 數據分析與結果討論 57
4.2 單層石墨烯薄板在非局域性彈性理論之統御方程建立 58
4.2.1 無因次方程與EFG解 59
4.2.2 數據分析與結果討論 61
4.3 靜電驅動微/奈米石墨烯薄板致動器之統御方程建立 62
4.3.1 無因次方程與EFG解 64
4.3.2 數據分析與結果討論 66
第五章 總結與展望 85
5.1 總結 85
5.2 展望 86
參考文獻 87

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