臺灣博碩士論文加值系統

雷射干涉重力波偵測器是運用於直接量測重力波存在與否以證明廣義相對論以及開發重力波天文學之重要儀器設備。由於重力波訊號極其微弱，因此需有效降低系統中的各種雜訊才能進行重力波觀測，而系統整體最為靈敏的頻率範圍中以光學薄膜熱擾動所造成的雜訊影響最大。一般以量測機械損耗並藉由統計力學中的Fluctuation dissipation theorem間接得到熱擾動資訊。而欲探討薄膜之機械損耗時，需將薄膜鍍製於本身機械損耗相當低的基板，目前重力波偵測系統是以熔融石英玻璃作為基板，矽基板為下一世代偵測器基板之主要候選材料。考慮重力波偵測系統最靈敏之頻率範圍約在40~400Hz，因此本研究使用矽基板，並製成第一模態之共振頻率在此範圍內的懸臂樑狀。
本論文即是針對矽懸臂樑基板進行探討，包含懸臂樑尺寸設計，以ANSYS模擬各共振模態之頻率、振形，利用機械損耗量測系統進行各模態之損耗量測，將量測結果與暫態分析模擬結果相互比較，以完整建立ANSYS模態、暫態分析模擬及高頻模態機械損耗量測之流程。另一部分則是針對造成機械損耗測量誤差進行分析，統計各共振模態之重覆夾持誤差大小及探討誤差來源。實驗室主要研究為探討各種薄膜材料之機械損耗，其需由量測鍍膜前後試片之機械損耗搭配應變能比而計算出，其中應變能比能以理論公式及模擬求得，而本論文另一部分為建立ANSYS模擬應變能比之流程。

摘要 I
致謝 II
圖目錄 V
表目錄 VII
第一章 導論
1-1前言 1
1-2 研究動機 2
第二章 有限元素法基本理論
2-1 有限元素法簡介 5
2-2 系統運動方程式 7
2-2.2 ANSYS暫態分析 11
第三章 單晶矽懸臂樑ANSYS模態分析模擬流程及結果
3-1矽懸臂樑模態分析 15
3-1.1 尺寸設計 15
3-1.2 共振模態模擬 17
3-2 含薄膜之矽懸臂樑Strain energy ratio分析 20
3-2.1 單層薄膜Strain energy ratio分析 23
3-2.2多層薄膜Strain energy ratio分析 24
第四章 單晶矽懸臂樑機械損耗量測流程及結果
4-1 機械損耗量測系統介紹 27
4-1.1 機械損耗理論 27
4-1.2 機械損耗量測系統架構 31
4-2 矽懸臂樑製作方式 35
4-3 矽懸臂樑彎曲及扭轉模態判別方式 36
4-4 機械損耗量測系統之量測誤差分析 40
4-4.1 矽懸臂樑表面分析 40
4-4.2 夾持矽懸臂樑之夾具表面分析 42
4-4.3 矽懸臂樑各共振模態之re-clamp error統計結果 45
4-5 矽懸臂樑各共振模態之機械損耗 51
第五章 單晶矽懸臂樑ANSYS暫態分析模擬
5-1矽懸臂樑阻尼之量測 54
5-2 矽懸臂樑模擬機械損耗分析 56
第六章 結論
6-1 結果討論 58
6-2 未來展望 59
附錄A. ANSYS共振模態模擬流程 60
附錄B. ANSYS strain energy模擬流程 70
附錄C. ANSYS共振模態模擬command 85
附錄D. ANSYS暫態分析command 87
附錄E.高頻量測機械損耗SOP 95
參考文獻 99

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