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研究生:楊文佩
研究生(外文):Wen-Pei Yang
論文名稱:可調式聲子晶體元件之分析與設計
論文名稱(外文):Analysis and Design of Tunable Phononic Crystal Devices
指導教授:陳聯文
指導教授(外文):Lien-Wen Chen
學位類別:博士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:中文
論文頁數:122
中文關鍵詞:可調式平面波展開法聲子晶體
外文關鍵詞:plane wave expansionphononic crystalstunable
相關次數:
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  • 收藏至我的研究室書目清單書目收藏:0
聲子晶體是由兩種不同的彈性材料或流體週期排列而組成的結構,此人造物質有聲子能隙的特殊現象,可阻絕聲波或彈性波在聲子晶體上的傳遞。聲子能隙的位置與大小由聲子晶體之組成材料、排列方式及晶格間距來決定;當聲子晶體的組成材料及排列方式決定後,其能隙的頻率範圍即可定義出來。為了得到可調變的聲子能隙,本文以介電彈性體當作聲子晶體的填充柱,以其電致動特性來設計可調式之聲子晶體元件。介電彈性體是一種智慧材料,在外加電場的作用下可產生極大的應變,是微小型致動器的最佳材料。利用介電彈性體的致動應變,以外加電場來控制聲子晶體的能隙範圍,本文使用平面波展開法及有限元素分析軟體分析聲子能帶的分佈,並以數值分析結果驗證其主動控制的特性。
使用空心圓柱致動器當作聲子晶體的填充柱,在電場的作用下可調變聲子晶體的部份與絕對能隙,並可利用此調變特性應用於聲波開關或濾波器的設計上;此外,本文還使用伸縮型致動器組成聲子晶體結構,討論電場大小與聲子能隙的變化。因伸縮型致動器在電場的作用,其截面形狀由正方形變化為長方形,所以可利用此致動器組成聲子晶體之異質結構;使用不同方位角所組的異質結構,在電場作用下,可產生新的聲子能隙。可調式聲子晶體由介電彈性體所組成,可得到良好的調變效果,並有快速的反應時間可滿足快速控制的需求。
聲子晶體結構除了聲子能隙的特殊性質外,其負折射現象也是目前重要的研究主題。本文以平面波展開法求得二維聲子晶體的等頻圖,並討論聲波頻率、入射角度與其折射角的關係,並使用有限元素軟體模擬聲波在聲子晶體的波傳現象。因介電彈性的致動效應,可利用外加電場來改變介電填充柱的尺寸,進而主動控制聲波入射聲子晶體的折射角度,使其折射角度在正負之間變化;且聲波入射角度越大,可得到越大的折射角度變化。負折射現象可應用在聲子晶體平面透鏡的設計,聲波源透過平面透鏡而在另一端聚焦成像;利用介電彈性體所組成的聲子晶體平面透鏡,在固定其厚度與波源距離的情況下,以外加電場改變聲波源的聚焦位置,設計出可調式負折射平面透鏡。可調式聲子晶體元件可應用在未來生醫科技及高精密儀器的隔振系統上。
Phononic crystals are artificial structures in which the periodic variation of densities and material properties gives rise to stop band for elastic/acoustic wave within a certain frequency. We study the tunable acoustic band gaps of a two-dimensional sonic crystal with dielectric elastomer actuators. Dielectric elastomer is a novel material and is able to generate large strain by transforming the electrical energy directly into the mechanical work. The geometry of dielectric elastomer actuator can be changed under the action of electric field. We investigated the properties of the tunable sonic crystal devices with dielectric elastomer actuator by using the plane wave expansion and the finite element method. Calculating the transmission coefficients by finite element software, the acoustic band gaps of a sonic crystal with cylindrical actuators could be tuned with the different electric field. The narrow pass band and partial band gaps can be controlled by applying electric field and various tunable sonic crystal devices can be realized by using dielectric elastomer actuators.
The band structure of a 2D sonic crystal with extender actuators is also investigated. The dielectric elastomer extender actuator is made of a square rod sandwiched between two compliant electrodes. The band gaps of sonic crystals with extender actuators can be tuned by applying an electric field. The band structures of hetero-structure sonic crystals consisting of extender actuators are investigated. The narrow stop bands can be created in the presence of an electric field.
The refractive and focusing behaviors of a tunable sonic crystal with dielectric elastomer actuators are also investigated. The refractive direction of the acoustic wave in sonic crystals is predicted from the equivalent frequency surface obtained by plane-wave expansion method. The dispersion relation is varied with the geometric adjustment of the dielectric elastomer actuator and the refractions of acoustic wave in sonic crystals are changed from positive to negative with the increase of applied electric field. Based on the geometry adjustment of the actuator, a tunable acoustic superlens could be proposed by a sonic-crystal slab with dielectric elastomer tubes. The distance from the surface of the slab to the center of the image spot can be changed with different electric field. Thus, extensive applications of such a phenomenon to acoustic device are anticipated.
目 錄

摘 要 I
Abstract III
誌 謝 V
目 錄 VI
表 目 錄 VIII
圖 目 錄 IX
符號說明 XIV
第一章 緒論 1
1-1 前言及研究目標 1
1-2 研究動機及分析模型 4
1-3 文獻回顧 6
1-3.1 基本的聲子晶體 6
1-3.2 可調式聲子晶體 9
1-3.3 聲子晶體負折射 12
1-4 本文架構 14
第二章 介電彈性體 23
2-1 前言 23
2-2 介電彈性體操作原理 23
2-3 介電致動器之理論分析 25
2-3.1 伸縮型致動器 26
2-3.2 空心圓柱致動器 27
第三章 數值計算方法 39
3-1 前言 39
3-2 固態物理學基本定義 40
3-2.1 倒晶格空間 40
3-2.2 布里淵區(Brillouin Zones) 41
3-2.3 布洛赫定理(Bloch theorem) 43
3-3 平面波展開法 44
3-3.1 正方晶格排列 47
3-3.2 三角晶格排列 47
3-4 有限元素法 48
3-4.1 聲波模組之有限元素法 48
3-4.2 多重物理量的耦合問題 51

第四章 聲子晶體之色散關係 59
4-1 前言 59
4-2 實心與空心圓柱之二維聲子晶體結構 60
4-3 含介電彈性體之聲子晶體 63
4-3.1 空心圓柱致動器 63
4-3.2 方形柱致動器 65
第五章 聲子晶體之負折射現象 85
5-1 前言 85
5-2 等頻圖與折射角之判斷 85
5-3 聲子晶體折射波種類 86
5-4 聲子晶體負折射現象之分析與模擬 87
5-4.1 聲子晶體負折射現象 87
5-4.2 可調式負折射聲子晶體 88
5-4.3 聲子晶體的聚焦現象 89
5-4.4 可調式聲子晶體平面透鏡 90
第六章 綜合結論與未來展望 105
6-1 綜合結論 105
6-2 未來研究方向與建議 106
參考文獻 109
自 述 121
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