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系統識別號 U0026-1408202014590000
論文名稱(中文) 附有雙螺旋局部共振器之結構樑動態分析
論文名稱(英文) Dynamic Analysis of a Beam with Double-Spiral Locally Resonant Systems
校院名稱 成功大學
系所名稱(中) 工程科學系
系所名稱(英) Department of Engineering Science
學年度 108
學期 2
出版年 109
研究生(中文) 陳宗毓
研究生(英文) Tzung-Yu Chen
電子信箱 adsl41011@gmail.com
學號 N96071287
學位類別 碩士
語文別 中文
論文頁數 101頁
口試委員 指導教授-陳蓉珊
口試委員-周榮華
口試委員-潘文峰
口試委員-王榮泰
口試委員-劉立偉
中文關鍵字 超穎材料  能隙  負質量效應  雙螺旋型共振器 
英文關鍵字 metamaterial  negative mass effect  band gap  double-spiral locally resonant systems 
學科別分類
中文摘要 超穎材料為一種具有天然材料所不具備之超常物理性質之人工結構或複合材料,其超常物理性質可能包括負質量、負折射率、負體積模數等,且其性質往往不決定於構成材料本身,而決定於其中的人工構造。超穎材料之概念一開始被應用在電磁波領域,近年來逐漸拓展到聲學及彈性波領域。透過特殊設計之負質量超穎材料結構單元使的波傳在特定頻段之衰減達到減振之目的。
本文建立一具有負質量效應之結構單元,其可以分為中央鏤空主樑與嵌在該主樑內部之子結構,該子結構為一附有中央質量塊之雙螺旋結構樑。透過有限元素軟體COMSOL模擬該結構單元之波傳現象,驗證其負質量效應之發生,並觀察頻散曲線中之結構模態得知其能隙與負質量效應之產生原因為子結構之共振現象。本文提出兩種理論模型計算子結構之自然共振頻率,計算結果皆與模擬大致相吻合,且自然共振頻率均落在負質量效應與能隙之起始位置附近。
增加子結構之質量塊可以有效降低子結構共振頻率,因此,本研究透過調整質量塊厚度或是子結構樑的厚度、寬度來控制結構之共振頻率,並觀察相對應結構單元之頻散曲線與負質量效應之變化,結果顯示改變質量塊厚度後之子結構共振頻率亦可以大致吻合負質量效應與能隙之起始位置,從而達到調控結構之減振區頻段的目的。
英文摘要 This thesis presents a novel metamaterial beam with periodic substructures. Each cell consisted of two parts: a host beam with central hole and a substructure embedded in it. The substructure is comprised of a double-spiral beam with a central mass. With the finite element software COMSOL Multiphysics, the dynamic behavior of the metamaterial beam is investigated. The simulated results demonstrated that the band gap and negative mass exist in such a structure. Moreover, two theoretical models were proposed to calculate the natural frequency of the substructure. Both calculations approximately matched with simulation results. The error is less than 5%. The natural frequency of the substructure was close to the starting frequency of the band gap. By adjusting dimensions of the substructure, control of the vibration attenuation zone in the structure can be achieved.
論文目次 中文摘要 (I)
Extend Abstract (II)
致謝 (IX)
目錄 (X)
表目錄 (XIV)
圖目錄 (XVI)
符號 (XIX)
第一章 導論(1)
1.1 研究動機(1)
1.2 文獻回顧(1)
1.3 章節介紹(5)
第二章 有限元素理論(6)
2.1 空間中樑的剛度矩陣與質量矩陣(6)
2.1.1 節點座標中樑的自由度(6)
2.1.2 樑元素的剛度矩陣(7)
2.1.3 樑元素的質量矩陣(9)
2.2 座標轉換矩陣(10)
2.3 組合矩陣(12)
2.3.1 起始樑初始端固定之邊界條件(16)
2.3.2 末端樑末端固定之邊界條件(17)
2.3.3 起始樑初始端與末端樑末端固定之邊界條件(19)
2.4 末端質量塊之動態分析(20)
2.4.1 質量塊之質量矩陣(20)
2.4.2 含質量塊之系統矩陣(21)
2.5 自由振動分析(23)
第三章 連續系統理論(24)
3.1 尤拉樑之統御方程式(24)
3.1.1 分離變數法解撓度方程式(24)
3.1.2 尤拉樑扭轉統御方程式(25)
3.1.3 分離變數法解扭轉方程式(25)
3.2 邊界條件(28)
3.2.1 初始樑初始自由(28)
3.2.2 初始樑初始固定[29](29)
3.2.3 最末樑末端自由[29](30)
3.2.4 最末樑末端固定(31)
3.3 連續條件(33)
3.3.1 順時鐘排列連續條件[29](33)
3.3.2 逆時鐘排列連續條件(38)
3.3.3 直線排列連續條件(42)
3.4 外加質量塊之力學條件(49)
3.4.1 末端質量塊之邊界條件(49)
3.4.2 中央質量塊之連續條件(51)
3.5 自由振動分析(56)
3.5.1 遞迴關係式[29](56)
3.5.2 系統矩陣[29](57)
第四章 有限元素模擬與結果分析(58)
4.1 雙螺旋形局部共振器之結構幾何與材料參數(58)
4.1.1 順時鐘排列螺旋形結構樑幾何(59)
4.1.2 逆時鐘排列螺旋形結構樑幾何(61)
4.1.3 中央質量塊幾何(62)
4.2 有限元素理論與模擬結果(63)
4.2.1 螺旋形結構樑收斂分析(63)
4.2.2 螺旋形結構樑之自然共振頻率(66)
4.2.3 樑末端質量塊收斂分析(66)
4.2.4 樑末端質量塊之自然共振頻率(68)
4.2.5 雙螺旋樑-質量局部共振器收斂分析(70)
4.2.6 雙螺旋樑-質量局部共振器之自然共振頻率(72)
4.2.7 改變結構尺寸之理論結果(73)
4.3 連續體理論與模擬結果(78)
4.3.1 順時鐘排列螺旋形結構樑之自然共振頻率(78)
4.3.2 逆時鐘排列螺旋形結構樑之自然共振頻率(79)
4.3.3 樑末端質量塊之自然共振頻率(80)
4.3.4 雙螺旋樑-質量局部共振器之自然共振頻率(82)
4.3.5 改變結構尺寸之理論結果(83)
4.4 附有雙螺旋形局部共振器之結構單體之動態模擬(86)
4.4.1 附有雙螺旋形局部共振器之結構單體幾何尺寸(86)
4.4.2 含局部共振器之結構單體收斂分析(86)
4.4.3 頻散曲線(89)
4.4.4 等效面質量密度(90)
4.5 結構單元不同幾何尺寸下之模擬結果(93)
4.5.1 頻散曲線(93)
4.5.2 等效面質量密度(94)
第五章 結論與未來展望(96)
5.1 結論(96)
5.2 未來展望(97)
參考文獻(98)
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