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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 馬劍清 | |
| dc.contributor.author | YAO-CHUNG CHANG | en |
| dc.contributor.author | 張耀中 | zh_TW |
| dc.date.accessioned | 2021-06-08T05:12:58Z | - |
| dc.date.issued | 2006 | |
| dc.date.submitted | 2006-07-15 | |
| dc.identifier.citation | 參考文獻
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Wu, H. F. Hu, et al., “Large acoustic band gaps created by rotating square rods in two-dimensional periodic composites,” J. Phys. D: Appl. Phys., 36(1), L15~L17, JAN 7, (2003). [35] X. Zhang, Z. Y. Liu, J. Mei, Y. Y. Liu, “Acoustic band gaps for a two-dimensional periodic array of solid cylinders in viscous liquid,” J. Phys.: Condens. Matter, 15, 8207~8212, (2003). [36] X. H. Hu, Y. F. Shen, X. H. Liu, R. T. Fu, J. Zi, “Complete band gaps for liquid surface waves propagating over a periodically drilled bottom,” Phys. Rev. E, 68, 066308-1~066308-5, (2003). [37] Y. Y. Chen, Z. Ye, “Acoustic attenuation by two-dimensional arrays of rigid cylinders,” Phys. Rev. Lett., 87(18), 184301-1~184301-4, (2001). [38] Y. Cao, Z. Hou, Y. Liu, “Convergence problem of plane-wave expansion method for phononic crystals,” Phys. Lett. A, 327, 247~253, (2004). [39] 林斯親，二維聲子晶體波傳與頻溝現象之研究，台灣大學應用力學研究所碩士論文，台北市，2000年。 [40] 林宜賢，聲子晶體應用於水中吸音材料之可行性研究，中山大學機械與機電工程學所碩士論文，台北市，2005年。 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/23950 | - |
| dc.description.abstract | 聲子晶體的頻帶間隙特性在表面聲波元件上有很多應用。本文研究了複式晶格聲子晶體的頻帶結構特性。應用平面波展開法（PWM）計算複式晶格聲子晶體頻帶結構，本文採用二維鎳合金/空氣體系，計算了以蜂窩格子和Kagome格子為代表的複式晶格的頻帶結構；並與正方晶格和三角晶格為代表的簡單晶格的結果作了相互比較分析，結果顯示，在某些填充率範圍內，將聲子晶體排列為複式晶格要優於簡單晶格，可以得到更寬的頻溝。此外，借助於頻溝分佈圖，分析了頻溝數目、頻溝寬度以及頻溝上下邊界頻率隨填充係數的變化特性。
文中亦應用時域有限差分方法（FDTD）來分析頻帶的特性，時域有限差分法是對偏微分波動方程的離散化處理，通過對時間和空間的離散化，將偏微分方程轉化為差分方程，繼而採用數值計算方法，求解波傳播過程中各個離散點的所有動態參數與時間的函數關係。時域有限差分方法（FDTD）不但可以計算週期結構中的頻帶結構而且可以計算有限結構的透射、反射等特性，且不受固液耦合、結構形式等因素的影響。 | zh_TW |
| dc.description.abstract | Frequency band gap characteristics of phononic crystals have many applications on the surface acoustic wave device. In this thesis, we investigate frequency band structure characteristics in phononic crystals of multi-composition. We apply Plane Wave Method（PWM）to calculate frequency band structure in phononic crystals of multi-composition. Two-dimensional nickel/air system for the bee nest crystal and Kagome crystal are taken for numerical calculations of the frequency band structure in multi-composition. Then we make comparison with the results for simple crystal such as square and triangle crystal. The results show that we can get wider band gap with arranging the phononic crystal into multi-composition than simple crystal. In addition, we analyze the number and width of band gap and the characteristic of top and bottom boundary frequency of band gap varying with filling coefficient.
In this thesis, we also analyze characteristics of frequency band with Finite-Difference Time-Domain（FDTD）method. Finite-Difference Time-Domain method is to discrete partial differential wave equation by means of discrete to time and space. We transform partial differential equation into difference equation, then the numerical calculation method is used to solve the function relation of all dynamic parameter and time of each discrete point in the wave propagation process. Not only band structure in period structure is calculated but also characteristics of homology and reflection in finite structure is obtained. The FDTD method has the advantage that it can be applied to solve the coupled solid and liquid problem. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T05:12:58Z (GMT). No. of bitstreams: 1 ntu-95-R93522501-1.pdf: 860423 bytes, checksum: 2e7cd6a8bf6453b42288ffb49f1c5dab (MD5) Previous issue date: 2006 | en |
| dc.description.tableofcontents | 目 錄
誌謝 ....................................................................................................................I 中文摘要 ...........................................................................................................II 英文摘要 .........................................................................................................III 目錄 ..................................................................................................................V 表目錄 ..........................................................................................................VIII 圖目錄 ............................................................................................................IX 符號表 ...........................................................................................................XII 第一章 緒論 ...................................................................................................1 1-1 前言 ......................................................................................................1 1-2 文獻回顧 ..............................................................................................1 1-2-1 理論部份 .......................................................................................1 1-2-2 實驗部份 .......................................................................................4 1-3 研究動機與內容簡介 ..........................................................................5 第二章 二維聲子晶體的理論架構 ...............................................................8 2-1 週期性晶格結構 ..................................................................................8 2-2 一維聲波 ............................................................................................11 2-3 二維晶格種類 ....................................................................................14 2-4 晶體晶格與倒晶格（Reciprocal Lattice）.........................................15 2-5 填充率（Filling Fraction）..................................................................16 2-6 布洛赫理論（Bloch theorem）...........................................................17 2-7 布拉格定理（Bragg Law）.................................................................17 2-8 布里淵區（Brillouin Zone）...............................................................20 2-9 [100]與[110]方向指數 .......................................................................21 2-10 平面波展開法（Plane Wave Expansion, PWE）.............................22 2-11 任意週期性結構的平面波展開法....................................................24 2-12 頻帶結構 ..........................................................................................25 2-13 頻溝展生的機制 ..............................................................................26 第三章 複式結構聲子晶體的頻溝結構特性 .............................................29 3-1 平面波展開法計算複式晶格頻帶結構的分析 ................................29 3-1-1 基本的假設條件 .........................................................................30 3-1-2 數學模式與理論推導 .................................................................30 3-1-3 四種結構的布里淵區 .................................................................32 3-2 數值計算結果及分析 ........................................................................33 3-2-1 二維鎳合金/空氣體系 ...............................................................34 3-2-2 複式晶格分佈頻溝與簡單晶格的對比分析 .............................35 3-2-3 複式晶格頻溝分佈圖的出現頻溝分析 .....................................35 3-2-4 各晶格第一條頻溝寬度 隨填充係數 的變化分析 ...........36 3-3 複式晶格頻溝分佈的綜合探討 ........................................................37 第四章 聲子晶體頻溝計算中的時域有限差分方法 .................................52 4-1 時域有限差分方法（FDTD）簡介 .................................................52 4-2 理論架構推導 ....................................................................................52 4-2-1 模型描述及基本方程 .................................................................52 4-2-2 交錯網格FDTD的算法 ............................................................54 4-2-3 差分方程 .....................................................................................55 4-2-4 時間條件 .....................................................................................56 4-2-5 穩定性判斷 .................................................................................56 4-2-6 空間邊界條件 .............................................................................57 4-3 數值計算過程 ....................................................................................57 4-3-1 實例計算結果 .............................................................................58 4-3-2 計算結果討論 .............................................................................59 4-3-3 對比分析與推衍到其他常用金屬 .............................................60 4-4 結論 ....................................................................................................61 第五章 結論與未來展望 .............................................................................76 5-1 結論 ....................................................................................................76 5-2 未來展望 ............................................................................................77 參考文獻 .........................................................................................................78 作者簡歷 .........................................................................................................85 | |
| dc.language.iso | zh-TW | |
| dc.title | 二維聲子晶體在複式晶格結構與時域
有限差分法分析頻溝之探討 | zh_TW |
| dc.title | Band Gaps Analysis for Two-Dimensional Phononic
Crystals in Multi-Composition Using Finite-Difference Time-Domain Method | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 94-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 吳政忠,尹慶中 | |
| dc.subject.keyword | 頻帶間隙,平面波展開法,時域有限差分方法, | zh_TW |
| dc.subject.keyword | Frequency band gap,Plane Wave Method,Finite-Difference Time-Domain method, | en |
| dc.relation.page | 84 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2006-07-17 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 機械工程學研究所 | zh_TW |
| 顯示於系所單位： | 機械工程學系 | |
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