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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/62209完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 宋家驥 | |
| dc.contributor.author | Chi Lin | en |
| dc.contributor.author | 林奇 | zh_TW |
| dc.date.accessioned | 2021-06-16T13:33:57Z | - |
| dc.date.available | 2018-07-26 | |
| dc.date.copyright | 2013-07-26 | |
| dc.date.issued | 2013 | |
| dc.date.submitted | 2013-07-18 | |
| dc.identifier.citation | [1] E. Yablonovitch, 'Inhibited spontaneous emission in solid-state physics and electronics,' Phys. Rev. Lett. 58, 2059-2062 (1987).
[2] S. John, 'Strong localization of photons in certain disordered dielectric superlattices,' Phys. Rev. Lett. 58, 2486-2489 (1987). [3] S. Tamura, D. C. Hurley, and J. P. Wolfe, 'Acoustic-phonon propagation in superlattices,' Phys. Rev. Rev. B 38(2), 1427-1449 (1998). [4] M. S. Kushwaha, P. Halevi, G. Martinez, L. Dobrzynski, and B. Djafari-Rouhani, 'Theory of acoustic band structure of periodic elastic composites,' Phys. Rev. Rev. B 49(4),2313-2322 (1994). [5] R. Martínez-Sala, J. Sancho, J. V. Sánchez, 'Sound attenuation by sculpture,' Nature (London) 378,241 (1995). [6] X. Zhang, and Z. Liu, 'Negative refraction of acoustic waves in two-dimensional phononic crystals,' Appl. Phys. Lett. Vol. 85, No. 2, pp. 341-343 (2004). [7] M. H. Lu, C. Zhang, L. Feng, J. Zhao, Y. F. Chen, Y. W. Mao, J. Zi, Y. Y. Zhu, S. N. Zhu, and N. B. Ming, 'Negative birefraction of acoustic waves in a sonic crystal,' Nat. Mater. Vol. 6, No. 10, pp. 744-748 (2007). [8] L. Y. Wu, 'The Foci and Dispersions of Negative Refraction Sonic Crystals with Circular and Elliptic Rods,' Master thesis (2007) Tainan: Cheng Kung University, Taiwan. [9] Liang Feng, Xiao-Ping Liu, Ming-Hui Lu, Yan-Bin Chen, Yan-Feng Chen, Yi-Wei Mao, Jian Zi, Yong-Yuan Zhu, Shi-Ning Zhu, and Nai-Ben Ming, 'Refraction control of acoustic waves in a square-rod-constructed tunable sonic crystal,' Phys. Rev. B 73, 193101 (2006). [10] Chunyin Qiu and Zhengyou Liu, 'Acoustic directional radiation and enhancement caused by band-edge states of two-dimensional phononic crystals,' Phys. Rev. B 79, 094302 (2006). [11] S.-C.S. Lin, T. J. Huang, J.-H. Sun, and T.-T. Wu, 'Gradient-index phononic crystals,' Phys. Rev. B 79, 094302. [12] S.-C.S. Lin, B. R. Tittmann, J.-H. Sun, T.-T. Wu, and T. J. Huang, 'Acoustic beamwidth compressor using gradient-index phononic crystals,' J. Phys. D: Appl. Phys. 42, 185502 (2009). [13] S.-C.S. Lin, B. R. Tittmann, J.-H. Sun, and T. J. Huang, 'Design of acoustic beam aperture modifier using gradient-index phononic crystals,' J. Appl. Phys. 111, 123510 (2012). [14] S.-C.S. Lin and T. J. Huang, 'Acoustic mirage in two-dimensional gradient-index phononic crystals,' J. Appl. Phys. 106, 053529 (2009). [15] Ke Deng, Yiqun Ding, Zhaojian He, Heping Zhao, Jing Shi, and Zhengyou Liu, 'Graded negative index lens with designable focal length by phononic crystal,' J. Phys. D: Appl. phys. 42 (2009). [16] Alfonso Climente, Daniel Torrent, and Jose Sanchez-Dehesa, 'Sound focusing by gradient index sonic lenses,' Appl. Phys. Lett. 97, 104103 (2010). [17] Theodore P. Martin, Michael Nicholas, Gregory J. Orris, Liang-Wu Cai, Daniel Torrent, 'Sonic gradient index lens for aqueous applications,' Appl. Phys. Lett. 97, 113503 (2010). [18] Yan-Ting Chen, 'Focusing behavior of plate wave by using gradient-index phononic crystal,' Master thesis (2011). Taipei: Taiwan University, Taiwan. [19] M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani, 'Acoustic band structure of periodic elastic composites,' Phys. Rev. Lett. Vol. 71, No. 13, pp. 2022-2025 (1993). [20] M. S. Kushwaha, 'Classical band structure of periodic elastic composites,' Int. J. Mod. Phys. B Vol. 10, No. 9, pp. 977-1094 (1996). [21] M. S. Kushwaha, and B. Djafrari-Rouhani, 'Giant sonic stop band in two-dimensional periodic system of fluids,' Journal of Applied Physics Lett Vol. 84, No. 9, 4677 (1998). [22] A. Khelif, P. A. Deymier, B. Djafari-Rouhani, J. O. Vasseur, and L. Dobrzynski, 'Two-dimensional phononic crystal with tunable narrow pass band: Application to a waveguide with selective frequency,' J. Appl. Phys. Vol. 94, No.3, 1308 (2003). [23] COMSOL Multiphysics User’sGuide and Modeling Guide. [24] J. N. Reddy, 'An introduction to the finite element method 3rd ed.McGraw-Hill, ' New York (2006). [25] X. Zhang, and Z. Liu, 'Negative refraction of acoustic waves in two-dimensional phononic crystals,' Appl. Phys. Lett. Vol. 85, No. 2, 341 (2004). [26] S. C. Lin,'Ultrasonic Band gap of 2-D phononic crystal,' Master dissertation, Taipei: Nation Taiwan University, Taiwan. (2001). [27] D. N. Chigrin, S. Enoch, C.M. Sotomayor Torres, and G. Tayeb, Opt. Express 11, 1203 (2003). [28] Chen-Che Tsai, 'Acoustic wave propagation of tunable two-dimensional phononic crystal,' Master thesis, Taipei: Nation Taiwan University, Taiwan. (2011). [29] M. S. Kushwaha, P. Halevi, 'Band-gap engineering in periodic elastic composites,' Appl. Phys. Lett. Vol. 64, No.9, 1805 (1994). [30] M. S. Kushwaha, P. Halevi, G. Martínez, L. Dobrzynski, and B.Djafari-Rouhani, 'Theory of acoustic band structure of periodic elastic composites’, Phys. Rev. B. Vol.49, No. 4, 2313 (1994). [31] M. S. Kushwaha, P. Halevi, 'Giant acoustic stop bands in two-dimensional periodic arrays of liquid cylinders,' Appl. Phys. Lett. Vol.69, No. 1, 31 (1996). [32] M. S. Kushwaha, 'Stop-bands for periodic metallic rods: Sculptures that can filter the noise,' Appl. Phys. Lett. Vol. 70, No. 24, 3218 (1997). [33] J. O. Vasseur, P. A. Deymier, A. Khelif, B. Djafrari-Rouhani, A. Akjouj, L. Dobrzynski, N. Fettouhi, and J. Zemmouri, 'Phononic crystal with low filling fraction and absolute acoustic band gap in the audible frequency range: A theoretical and experimental study,' Phys. Rev. E Vol. 65, No. 5, 056608 (2002). [34] Y. Pennec, B. Djafari-Rouhani, J. O. Vasseur, A. Khelif, and P. A. Deymier, 'Tunable filtering and demultiplexing in phononic crystals with hollow cylinders,' Phys. Rev. E. Vol. 69, No.4, 046608 (2004). [35] M. Ruzzene and A. Baz, 'Control of wave propagation in periodic composite rodsusing shape memory inserts,' Journal of Vibration and Acoustics Vol. 122, No. 2, 151 (2000). [36] M. Ruzzene and A. Baz, 'Attenuation and localization of wave propagation in periodic rods using shape memory inserts,' Smart Materials and Structures Vol. 9, No.6 , 805 (2000). [37] M. Kafesaki, and E. N. Economou, 'Multiple-scattering theory for three-dimensional periodic acoustic composites,' Phys. Rev. B Vol. 60, No. 17, 11993 (1999). [38] 溫熙森, 溫激鴻, 郁殿龍, 王剛, 劉耀宗, 韓小雲, '聲子晶體,' 國防工業出版社 (2009). | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/62209 | - |
| dc.description.abstract | 類比於光子晶體，聲子晶體是週期性排列的散射子在基底中的結構。首先本文研究了二維圓柱及橢圓柱聲子晶體的頻散關係，包括帶隙、部分帶隙、以及定向傳播，然後是漸變折射率聲子晶體。利用平面波展開法得到頻帶結構，經由等頻曲線分析其波傳特性後，與有限元素法模擬做比較。
在不同的頻率下透過不同填充率或不同材料的聲子晶體下所對應的折射率都會不同，藉由光學漸變折射率的概念，設計了二維漸變折射率聲子晶體去操縱聲波的行進方向。 在這裡漸變折射率聲子晶體是由鋼柱週期排列成正方晶格，背景為空氣。透過平面波展開法來計算折射率，以及有限元素法來模擬波傳遞的現象。在二維聲子晶體徑向上透過改變不同旋轉角的橢圓柱，形成不同的折射率，用雙曲正割函數來設計折射率分佈，最後討論經由漸變折射率聲子晶體透鏡控制聲波聚焦的結果，包括不同層數及不同漸變係數的影響。以上二維聲子晶體波傳理論可進而發展至三維聲子晶體以及應用在未來的聲學元件與超音波儀器上。 | zh_TW |
| dc.description.abstract | Similar to photonic crystals, sonic crystals (SC) is a periodic array composed of scatters embedded in a host material. Here we study the dispersion characteristics of 2D sonic crystal with circular and elliptic rods first, including band gap, partial band gap and directional propagation, and then the gradient-index sonic crystals. The use of plane wave expansion method is to obtain the band structure. We compare the propagation characteristics analyzed by the equifrequecy surfaces with the simulation results by finite element method.
The refractive indexes for various filling fractions, materials or frequencies of a sonic crystals are all different. By the concept of gradient-index in optics, we designed a two-dimensional gradient-index (GRIN) sonic crystals to control the propagations of acoustic waves. The GRIN SC was composed of square array steel cylinders in the background of air. The refractive index is obtained by plane wave expansion method, and the wave propagation is simulated by finite-element method. Altering the rotation angles of the elliptic rods in 2D SC to make various refractive indexes and the refractive index distribution is designed as hyperbolic secant function. The results and discussions for different layers and gradient coefficient demonstrate the GRIN SC lens focusing behavior of acoustic wave. It is anticipated that this study may be applied in 3D acoustic assembled devices or in ultrasonic devices. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T13:33:57Z (GMT). No. of bitstreams: 1 ntu-102-R99525103-1.pdf: 9711558 bytes, checksum: ea756af9d1cc89832f61b418a225c266 (MD5) Previous issue date: 2013 | en |
| dc.description.tableofcontents | 目錄 I
誌謝 III 摘要 IV Abstract V 表目錄 VI 圖目錄 VII 第一章 緒論 1 1.1前言 1 1.2 研究動機 2 1.3文獻回顧 3 1.4本文架構 4 第二章 基礎理論 8 2.1 流體中的波動方程式 8 2.2 倒晶格空間 10 2.3 布里淵區 12 2.4 平面波展開法 [21,22] 13 2.5 有限元素法 17 2.5.1 聲學模組之有限元素法推導 [23, 24] 17 2.5.2 邊界條件 [24] 20 2.5.3 結構模組與聲學模組之耦合 [25] 20 第三章 聲子晶體頻散關係 29 3.1 聲子晶體帶隙計算 29 3.1.1聲子晶體模擬參數 29 3.1.2 圓柱聲子晶體 31 3.1.3 橢圓柱聲子晶體 38 3.2聲子晶體定向傳播 44 3.2.1 圓柱聲子晶體 44 3.2.2 橢圓柱聲子晶體 53 3.3 聲子晶體頻散關係結果與討論 64 第四章 漸變折射率聲子晶體 65 4.1 漸變折射率聲子晶體模擬參數 65 4.2 圓柱聲子晶體 66 4.2.1 圓柱聲子晶體聚焦與層數關係 68 4.2.2 圓柱聲子晶體聚焦與漸變係數關係 73 4.3 椭圓柱聲子晶體 77 4.3.1 椭圓柱聲子晶體聚焦與層數關係 79 4.3.2 椭圓柱聲子晶體聚焦與漸變係數關係 83 4.4 圓柱與椭圓柱漸變折射率聲子晶體比較 86 第五章 結論與未來展望 89 5.1 結論 89 5.2 未來展望 90 參考文獻 91 | |
| dc.language.iso | zh-TW | |
| dc.subject | 聲子晶體 | zh_TW |
| dc.subject | 漸變折射率 | zh_TW |
| dc.subject | 聚焦 | zh_TW |
| dc.subject | Focusing | en |
| dc.subject | Gradient index | en |
| dc.subject | Sonic crystals | en |
| dc.title | 橢圓柱聲子晶體漸變折射率聚焦與頻散關係之研究 | zh_TW |
| dc.title | Focusing by Gradient-index Sonic Crystals and Dispersion Characteristics with Elliptic Rods | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 黃維信,羅如燕,楊旭光,林益煌 | |
| dc.subject.keyword | 聲子晶體,漸變折射率,聚焦, | zh_TW |
| dc.subject.keyword | Sonic crystals,Gradient index,Focusing, | en |
| dc.relation.page | 95 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2013-07-18 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 工程科學及海洋工程學研究所 | zh_TW |
| 顯示於系所單位： | 工程科學及海洋工程學系 | |
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