聲子晶體傳導帶與週期性彈性柱波導之研究

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姓名

許顧鏹(Ku-Chaing Hsu) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

聲子晶體傳導帶與週期性彈性柱波導之研究
(Study on the conduction band of phononic crystal and periodic elasticity rods waveguide)

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摘要(中)

本論文使用平面波展開法與多重散射法，研究二維聲子晶體中彈性波的行為。由平面波展開法可得出二維聲子晶體中混合波與剪波的頻帶結構，以及無黏滯性流體組成之二維聲子晶體的純縱波頻帶結構，或者是由固體組成的二維聲子晶體之純剪波頻帶結構。我們根據對光子晶體中介電質柱波導之研究，提出與其相似的彈性柱波導結構。藉著引入超晶格，其頻帶結構可被計算，並可找出可傳播模態。我們也對彈性柱波導做彎曲角度變化以及無序排列，以研究其對於穿透率的影響。相信在將來，對於彈性波的應用上，此形式之波導能成為一有用的元件。

摘要(英)

In this thesis, we use plane wave expansion method (PWEM) and multiple scattering method to study the propagation behavior of elastic waves in the two-dimensional phononic crystals. The band structure of mixed (longitudinal-transverse) polarization mode and transverse polarization mode can be calculated using PWEM. The band structure for longitudinal polarization mode of two-dimensional phononic crystal composed of non-viscous fluid, and the band structure of transverse polarization mode of two-dimensional phononic crystal of solid can also be calculated. Inspired by the research of dielectric rods waveguide for guiding light, we propose elastic rods waveguide for guiding sound. The band structure of elastic rods waveguide is calculated using super-cell method, and the propagating mode can be obtained. We also consider the effect of bends and disorder on the transmission of the elastic rods waveguide. We believe that this kind of acoustic waveguide can useful in the future.

關鍵字(中)

★ 聲子晶體
★ 彈性柱波導
★ 介電質柱波導

關鍵字(英)

★ phononic crystal
★ periodic elasticity rods waveguide

論文目次

中文摘要 --------------------------------------------- Ⅰ
英文摘要 --------------------------------------------- Ⅱ
致謝 --------------------------------------------- Ⅲ
目錄 --------------------------------------------- Ⅳ
圖目錄 --------------------------------------------- Ⅴ
表目錄 --------------------------------------------- Ⅶ
第一章序論----------------------------------------- 1
第二章理論分析------------------------------------- 3
2-1 平面波展開法應用在聲子晶體------------------- 4
2-2 二維聲子晶體混合波、純剪波、純縱波頻帶結構--- 10
2-2-1 二維聲子晶體混合波頻帶結構------------------- 10
2-2-2 二維聲子晶體純縱波或純剪波頻帶結構----------- 11
2-3 二維聲子晶體超晶格--------------------------- 14
2-4 多重散射法----------------------------------- 16
2-5 多重散射法中能流計算------------------------- 22
第三章數值模擬------------------------------------- 27
3-1 二維聲子晶體混合波與剪波頻帶結構------------- 27
3-2 二維聲子晶體純縱波與純剪波頻帶結構----------- 31
3-3 超晶格於缺陷態頻帶結構----------------------- 34
第四章彈性柱波導研究與討論------------------------- 39
4-1 純縱波之彈性柱波導--------------------------- 40
4-2 純剪波之彈性柱波導--------------------------- 46
4-3 無序之分析與討論----------------------------- 56
4-3-1 無序對於純縱波之彈性柱波導其波導效應的影響--- 57
4-3-2 無序對於純剪波之彈性柱波導其波導效應的影響--- 61
第五章結論與未來展望------------------------------- 65
參考資料 --------------------------------------------- 67

參考文獻

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指導教授

欒丕綱(Pi-Gang Luan)

審核日期

2007-7-13

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