博碩士論文 101226019 詳細資訊




以作者查詢圖書館館藏 以作者查詢臺灣博碩士 以作者查詢全國書目 勘誤回報 、線上人數:8 、訪客IP:35.171.45.91
姓名 王大為(Da-wei Wang)  查詢紙本館藏   畢業系所 光電科學與工程學系
論文名稱 Dirichlet-to-Neumann映射法應用於多層結構柱之二維與三維聲子晶體頻帶結構之計算
(Band structure calculations with Dirichlet-to-Neumann map method for multi-shell-rods-in-fluid-background phononic crystals)
相關論文
★ 平坦化陣列波導光柵分析和一維光子晶體研究★ 光子晶體波導與藕合共振波導之研究
★ 光子晶體異常折射之研究★ 光子晶體傳導帶與介電質柱波導之研究
★ 平面波展開法在光子晶體之應用★ 偏平面光子晶體能帶之研究
★ 通道選擇濾波器之探討★ 廣義光子晶體元件之研究與分析
★ 新式光子晶體波導濾波器之研究★ 廣義非均向性介質的光傳播研究
★ 光子晶體耦合濾波器之研究★ 聲子晶體傳導帶與週期性彈性柱波導之研究
★ 對稱與非對稱波導光柵之特性研究★ 雙曲透鏡之研究
★ 電磁波與聲波隱形斗篷之研究★ 一維光子晶體等效非均向介值之研究
檔案 [Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   [檢視]  [下載]
  1. 本電子論文使用權限為同意立即開放。
  2. 已達開放權限電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。
  3. 請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。

摘要(中) 本篇論文使用Dirichlet to Neumann法來計算彈性波在由多殼層介質柱子與流體背景構成的聲子晶體之頻帶結構。傳統常用之平面波展開法 (plane wave expension) 在計算聲子晶體之頻帶時,若遇到固體與流體共存之系統,會由於固體區與流體區之波函數分量數量不同,而遭遇無法執行的困難。本論文使用之Dirichlet-to-Neumann法能夠輕易的藉由連接邊界條件來解決上述困難,並且大幅縮小計算資源。第二章首先介紹二維基本結構以及彈性波之基本理論,然後推導含有剪力波之彈性固體柱在在流體背景中之聲子晶體頻帶計算細節,以盡可能模擬真實情況。在第三章中,我們將原本的Dirichlet to Neumann法推廣至三維,並提出了可能的執行方法,以計算三維聲子晶體之頻帶。最後探討在二維結構中使用不同的殼層材料與厚度搭配對於聲波在週期介質中傳播情形之影響。
摘要(英) In this thesis the Dirichlet- to-Neumann map method is applied to the calculation of the band structure of the phononic crystal which consists of multi-shell rods and fluid background. Due to the inconsistency of the total number of dynamical wave variables in the solid and fluid regions of the phononic crystal, the conventional plane wave expansion method is not directly applicable. We thus turn to use the Dirichlet-to-Neumann map method to overcome such a problem. In chapter 2, we first introduce the typical structure of the phononic crystal and the basic theory of elastic waves, and then explain how to derive the wave fields in every region in a unit cell and give the calculation details for the band structures of the phononic crystals in the text and in the appendix. In order to mimic the real acoustic/elastic systems, in most calculations the shear waves are taken into account. In chapter 3, we then generalize the original Dirichlet-to-Neumann map method to 3D and propose a possible procedure for its implementation to the band structure calculations of 3D phononic crystals. Finally, we discuss the effects of the materials used in the phononic crystal and the thicknesses of the shells on the resultant band structures.
關鍵字(中) ★ 多層結構
★ 聲子晶體
★ DtN映射法
★ 頻帶結構
關鍵字(英) ★ Dirichlet-to-Neumann map method
★ band structure
★ multi-shell-rods
論文目次 目錄
摘要.......................................i
Abstract .................................ii
致謝......................................iii
目錄.......................................iv
圖目錄......................................v
第一章 簡介
1-1 光子晶體................................1
1-2 聲子晶體與聲波超材料.....................3
1-3 研究動機................................3
第二章 理論及計算方法
2-1 Dirichlet to Neumann method (DtN)
2-1-1 DtN 之電磁波能帶計算-二維系統...........5
2-1-2正方晶格...............................6
2-1-3三角晶格...............................9
2-2 二維DtN 聲子晶體
2-2-1聲子晶體理論計算.......................13
2-2-2加一層殼之結構.........................19
第三章 3D DtN 理論及計算方法
3-1-1 取點及座標設定 ...................26
3-1-2 求係數Al、Bl ...................27
3-1-3 簡單立方晶格 ....................29
3-1-4 Bloch定理化簡矩陣 ..............30
第四章 分析及模擬
4-1 二維固體柱流體背景......................34
4-2 二維多層結構DtN........................38
第五章 結論及展望...........................48
Appendix I................................49
Appendix II...............................65
參考文獻...................................68
參考文獻 [1] C. Kittle, Introduction to Solid State Physics, 7th Ed., John Wiley & Sons (2001)
[2] David K. Cheng, Field and wave electromagnetic, 2th Ed., Addison-Wesley
(1989)
[3] Zhengyou Liu, Xixiang Zhang, Yiwei Mao, Y. Y. Zhu,Zhiyu Yang, C. T. Chan,
Ping Sheng, Science, 289, 1734 (2000)
[4] Ping Sheng, X. X. Zhang, Z. Liu, C. T. Chan, Physica B. Condensed Matter, 338,
201 (2003)
[5] H.H. Huang a, C.T. Sun , G.L. Huang, International Journal of Engineering
Science, 47, 610 (2009)
[6] Wu Fu-Gen, Liu Zheng-You, Liu You-Yan, Chinese Phys. Lett., 18, 785 (2001)
[7] I. E. Psarobas, A. Modinos, R. Sainidou, N. Stefanou , Phys. Rev. B, 65, 064307
(2002)
[8] Ph. Lambin, A. Khelif, J. O. Vasseur, L. Dobrzynski, B. Djafari-Rouhani, Phys.
Rev. E, 63, 066605 (2001)
[9] Suxia Yang, J. H. Page, Zhengyou Liu, M. L. Cowan1, C. T. Chan, Ping Sheng,
Phys. Rev. Lett., 88, 104301 (2002)
[10] Liu ZY, Chan CT, Sheng P, Phys. Rev. B, 65, 165116 (2002)
[11] Zalipaev VV, Movchan AB, Poulton CG, et al., Proceedings of the Royal
Society of London series A-Mathematical Physical and Engineering Sciences,
458, 1887 (2002)
[12] Xin Zhang, Zhengyou Liub, Youyan Liua, Fugen Wu, Phys. Lett. A, 313, 455
(2003)
[13] Jensen JS, Journal of Sound and Vibration, 266, 1053 (2003)
[14] Hou ZL, Fu XJ, Liu YY, Phys. Lett. A, 317, 127 (2003)
[15] Wu FG, Liu ZY, Liu YY, Journal of Physics D-Applied Physics, 35, 162 (2002)
103
[16] Fugen Wu, Zhilin Hou, Zhengyou Liu, Youyan Liu, Solid State
Communications, 123, 239 (2002)
[17] Li XL, Wu FG, Hu HF, et al., Journal of Physics D-Applied Physics, 36, 15
(2003)
[18] Wu FG, Hou ZL, Liu ZY, et al., Phys. Lett. A, 292, 198 (2001)
[19] Wu FG, Liu ZY, Liu YY, Chinese Physics Letters, 18, 785 (2001)
[20] Sigmund O, Jensen JS, Philosophical Transactions of the Royal Society of
London Series A-Mathematical Physical and Engineering Sciences, 361, 1001
(2003)
[21] Cervera F, Sanchis L, Sanchez-Perez J V, Martinez-Sala R, Rubio C, Meseguer F,
Lopez C, Caballero D, Sanchez-Dehesa, J Phys. Rev. Lett., 88, 023902 (2001)
[22] Kuo C-H, Ye Z, J. Phys. D: Appl. Phys., 37, 2155 (2004)
[23] Kushwaha M S, Halevi P, Martinez G, Dobrzynski L, Djafari-Rouhani B, Phys.
Rev. B, 49, 2313 (1994)
[24] I. E. Psarobas,,N. Stefanou ,A. Modinos, Phys. Rev. B, 62, 278 (2000)
[25] S. Guo and S. Albin et. al. “Simple plane wave implementation for photonic crystal
calculations” Opt. Express Vol. 11, pp. 167-175, 2003.
[26] Dennis M. Sullivan, Electromagnetic Simulation Using The FDTD Method,
Wiley-IEEE Press, New York, 2001.
[27] Kane S.Yee et. al. “Numerical Solution of Initial Boundary Value Problems
Involving Maxwell’s Equations in Isotropic Media” , IEEE. Trans. Antennas.
Propag. ,Vol.14, pp. 302-307, 1966.
[28] O. C. Zienkiewicz, Robert Leroy Taylor, J. Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, Butterworth-Heinemann press, 2005.
[29] Rahman, B.M.A.; “A review on the characterization of photonic devices using the finite element method,” Electrotechnical Conference, 1996. MELECON ‘96., 8th
Mediterranean , vol.2, no., pp.705-708 vol.2, 13-16 May, 1996.
[30] Jianhua Yuan, Ya Yan Lu, J. Opt. Soc. Am. A, 23, 3217 (2006)
[31] 欒丕綱、陳啟昌,光子晶體:從蝴蝶翅膀到奈米光子學,五南出版社,台北市,民國九十九年。
[32] Arfken G B, Weber H J, Harris F, Mathematical Methods for Physicists, 6th Ed.,Academic Press (2005)
[33]Murray R. Spiegel ,Theory and problems of advanced mathematics for engineers & scientists. McGRAW-HILL (1983)
[34] Feng-Lian Li Yue-Sheng Wang and Chuanzeng Zhang, Phys. Scr. 84 (2011) 055402 (9pp)
指導教授 欒丕綱 審核日期 2015-1-29
推文 facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu   
網路書籤 Google bookmarks   del.icio.us   hemidemi   myshare   

若有論文相關問題,請聯絡國立中央大學圖書館推廣服務組 TEL:(03)422-7151轉57407,或E-mail聯絡  - 隱私權政策聲明