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研究生: 吳逸軒
Wu, Yi-Hsuan
論文名稱: 寬頻帶地震超材料設計與模擬
Design and numerical simulations of seismic metamaterials with broad-band gap
指導教授: 陳東陽
Chen, Tungyang
學位類別: 碩士
Master
系所名稱: 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年: 2018
畢業學年度: 106
語文別: 中文
論文頁數: 98
中文關鍵詞: 地震超材料局部共振帶隙
外文關鍵詞: seismic metamaterials, local resonance, band gap
相關次數: 點閱:114下載:11
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  • 由於地震超材料其特殊的減震方式,使得最近幾年內有不少學者投入該領域並開始探索與研究,而本文為了設計出能夠阻隔更寬頻的地震波之超材料,首先以彈簧質量系統去分析不同的材料層數與排列方式所組成的單元結構模型,然後找出最適合阻擋低頻波的單元結構,接著再以有限元素軟體建立該單元結構的連體模型,然後以真實材料的性質變化來觀察帶隙頻率範圍所受到的影響與趨勢,透過該趨勢可以設計出具有不同帶隙頻率範圍的單元結構並以一定數量排列組成地震超材料,最後再以全域模擬觀察地震超材料在帶隙範圍內的局部共振運動行為並驗證其寬頻帶的效果。

    Because of the shock absorption by the seismic metamaterials, many scholars have begun to study in this field and explore the physical insights in recent years. In order to design seismic metamaterials that are able to a block broad band gap of seismic waves, the spring-mass system is first used to analyze the unit structure model composed of different material layers and arrangements, and then a suitable model for blocking low-frequency waves is proposed. Referring to the results from the spring-mass system, we build up a continuum model and simulate the behavior by finite element analysis. The influence and trend of the stop frequency range are observed versus a variety of the parameters with the real materials. Seismic metamaterials are then designed that are composed of several unit structures with different band gap frequency range, and we can verify the effects of broad-band gap by the resonance behaviors in seismic metamaterials with broad-band gap.

    目錄 中文摘要 i Abstract ii 誌謝 viii 目錄 x 表目錄 xii 圖目錄 xiii 第一章 緒論 1 1.1 文獻回顧與相關研究 1 1.2 研究動機 4 1.3 論文簡介 5 第二章 局部共振與彈簧質量系統之等效負質量與能量分析 7 2.1 局部共振與彈簧質量系統簡介 7 2.2 一維彈簧質量系統之等效負質量 9 2.3 一維彈簧質量系統能量分析 13 第三章 二維多層彈簧質量系統頻散分析與比較 18 3.1 二維多層彈簧質量系統介紹 19 3.2 系統運動方程式與頻散方程式介紹 21 3.2.1 運動方程式建立 21 3.2.2 頻散方程式分析 24 3.3 材料順序配置與層數對頻帶的影響與比較 24 3.3.1 雙層彈簧質量系統頻帶分析 25 3.3.2 三層彈簧質量系統頻帶分析 28 3.3.3 四層彈簧質量系統頻散分析 31 3.4 層數比較 35 第四章 二維連體模型之參數變化對帶隙頻率範圍影響 38 4.1 單元結構種類的影響 39 4.1.1 數質模擬之參數設定 41 4.1.2 頻散圖分析 42 4.2 結構與材料尺寸的影響 45 4.2.1 單元結構整體尺寸變化 45 4.2.2 基質尺寸變化 46 4.2.3 內含物尺寸變化 49 4.3 材料性質的影響 54 4.3.1 基質密度與楊氏模數的變化 55 4.3.2 橡膠密度與楊氏模數的變化 57 4.3.3 鋼材密度與楊氏模數的變化 58 4.4 結果討論 61 第五章 超材料設計與二維全域模擬 62 5.1 超材料的設計想法 62 5.2 單元結構設計 64 5.3 單元結構排數對能量衰減的影響 67 5.3.1 半全域模型介紹 67 5.3.2 分析結果與討論 69 5.4 地震超材料全域模擬 74 5.4.1 全域模型參數設定與模擬結果 74 5.4.2 超材料內部的局部共振現象與討論 77 第六章 結論與未來展望 84 6.1 結論 84 6.2 未來展望 85 參考文獻 86 附錄A : 布拉格散射簡介 91 附錄B : 多層彈簧質量體系統運動方程通式推導 93 附錄C : 倒晶格與布里淵區簡介 96

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