
系統識別號 
U00262209201015464400 
論文名稱(中文) 
聲子晶體共振腔之分析與聲能能量擷取 
論文名稱(英文) 
Analysis and Acoustic Energy Harvesting of Resonant Cavity of Sonic Crystal 
校院名稱 
成功大學 
系所名稱(中) 
機械工程學系碩博士班 
系所名稱(英) 
Department of Mechanical Engineering 
學年度 
99 
學期 
1 
出版年 
99 
研究生(中文) 
吳亮諭 
研究生(英文) 
LiangYu Wu 
學號 
n1896113 
學位類別 
博士 
語文別 
中文 
論文頁數 
121頁 
口試委員 
指導教授陳聯文 召集委員羅裕龍 口試委員王清正 口試委員張怡玲 口試委員光灼華 口試委員鄭志鈞

中文關鍵字 
聲子晶體
共振腔
能量擷取

英文關鍵字 
sonic crystal
resonant cavity
energy harvesting

學科別分類 

中文摘要 
聲子晶體是由兩種或兩種以上不同的彈性材料或流體週期排列而形成的結構，此人造結構擁有聲子能隙的特殊現象，可隔絕聲波或彈性波在聲子晶體上的傳遞，使特定角度與頻率入射的聲波無法傳遞通過聲子晶體，可應用於濾波器或隔音裝置上。破壞完美聲子晶體的週期排列，將會在能隙範圍產生缺陷模態，在缺陷模態的頻率之下能夠將聲波或彈性波侷限在聲子晶體的缺陷之中，缺陷模態所對應的頻帶即為缺陷頻帶。移除一聲子晶體填充物形成聲子晶體的點缺陷，在其頻散曲線上會在能隙範圍內出現缺陷頻帶，此缺陷頻帶可視為穿透能帶，缺陷頻帶上的頻率可通過此含點缺陷聲子晶體；點缺陷亦可作為聲子晶體共振腔，共振腔的共振頻率即為缺陷頻帶的頻率。當入射聲波之頻率為共振頻率時，聲波將被侷限在共振腔之中，在共振腔中的聲波壓力將被大幅提升。
本文使用平面波展開法與超晶胞法計算含點缺陷聲子晶體之頻散曲線，並利用有限元素軟體計算週期結構之穿透頻譜與聲子晶體共振腔中的壓力，分析不同填充比與組成大小的聲子晶體共振腔，討論共振腔的聲壓放大特性與品質因子，並佐以實驗驗證之。本文亦再共振腔之中置入一赫姆霍茲共振器，形成局部共振缺陷，討論當聲子晶體共振腔與赫姆霍茲共振器結合時，共振器對於聲子晶體結構之波傳行為產生的影響，並與其他型態的缺陷作比較，本文以有限元素軟體結合週期性邊界來計算該結構的頻散曲線，並計算其穿透率，再實驗量測其穿透頻譜以驗證計算。有關含缺陷聲子晶體分析結果可應用在聲波濾波器上。
本文結合壓電材料與聲子晶體設計聲波產能裝置，利用聲子晶體共振腔將入射聲波聲壓放大的特性，使置於共振腔內的壓電材料產生振動，進而達到能量擷取的效果，即是利用噪音來產生電能，並以壓電理論推導壓電曲樑振動產生的輸出電壓與功率，進行能量擷取實驗，將其結果與理論作比較。利用聲子晶體可操縱聲波的特性，可同時完成能量擷取與噪音控制的目標，並擴展聲子晶體的應用面。

英文摘要 
Sonic crystals (phononic crystals) are periodic elastic composite materials. Such artificial crystals can exhibit acoustic or elastic band gaps in which sound and vibration are all forbidden in any direction, giving rise to prospective applications such as elastic/acoustic filters and noise/vibration isolations. One particularly interesting aspect of sonic crystals is the possibility of creating crystal defects to confine the elastic/acoustic waves in localized modes. Because of locally breaking the periodicity of the structure, the defect modes can be created within the band gaps, which are strongly localized around the local defect. The point defect is created by removing a single rod from the middle of the perfect periodic structure. There exist the defect bands in the absoulate band gap. The acoustic wave can propagate through the sonic crystal, since the defect band acts as a pass band in the band gap. The point defect can also act as the resonant cavity. At the frequency of the defect band, which is the resonant frequency, the acoustic waves should be localized in the resonant cavity and the pressures in the cavity are enhanced.
The plane wave expansion method and supercell calculation are adopted to calculate the band structure of the sonic crystal with a point defect. And, the finite element commerical software is employed to obtain the acoustic pressure in the middle of the cavity and transmission spectra of the sonic crystal. The effects of sizes and filling fractions are investigated, and the quality factor of the cavity is discussed. The transmission spectra and pressures in the defect of the sonic crystal are measured experimentally. The wave propagation of a twodimensional sonic crystal with a local resonant defect is also studied. The Helmholtz resonantor is placed at the point defect to be a local resonant defect. Band structures are calculated by using the finite element commerical software with periodic boundary condition. Band structures of the sonic crystal with a cavity, circular and Helmholtz resonant defect are discussed and compared. The transmission spectra are measured experimentally. The defect mode characteristics of the sonic crystal with a defect can be use in the implementations of new acoustic filters.
The development of an acoustic energy harvester using the sonic crystal and the piezoelectric material is presented. A point defect is created by removing a rod from a perfect sonic crystal. The point defect in the sonic crystal is acted as a resonant cavity, and the acoustic waves at the resonant frequency of the cavity can be localized in the cavity. The power generation from acoustic energy is based on the effect of the wave localization in the cavity of the sonic crystal and the direct piezoelectric effect of the piezoelectric material. A model for energy harvesting of the piezoelectric curved beam is also developed to predict the output voltage and power of the energy harvesting. The experimental results are compared with the theoretical ones. By using properties of band gaps and wave localizations of the sonic crystal, the noise control and energy harvesting can be achieved simultaneously.

論文目次 
摘要 I
Abstract II
誌謝 IV
目錄 V
表目錄 VIII
圖目錄 IX
符號說明 XV
第一章 緒論 1
11 前言 1
12 研究動機 1
13 文獻回顧 3
131 基本的聲子晶體 3
132 含缺陷聲子晶體 7
133 聲子晶體異常折射 8
134 能量擷取 10
14 本文架構 12
第二章 數值方法 15
21固態物理學基本定義 15
211倒晶格空間 15
212布里淵區(Brillouin Zones) 17
213布洛赫定理(Bloch theorem) 19
22平面波展開法 19
221正方晶格排列 22
222三角晶格排列 23
223 超晶胞法 24
23 有限元素法 25
第三章 聲子晶體共振腔 36
31 完美聲子晶體與含點缺陷聲子晶體 36
311 頻散曲線 36
312 穿透頻譜 37
32 聲子晶體共振腔 39
321 頻散曲線 39
322 共振腔壓力場模擬 40
33 聲子晶體共振腔實驗 41
331 聲子晶體之穿透頻譜 41
332 聲子晶體共振腔中心壓力量測 42
333 圓柱環繞聲子晶體共振腔中心壓力量測 45
第四章 含赫姆霍茲器之聲子晶體共振腔 65
41頻散曲線 65
42 含點缺陷聲子晶體之穿透頻譜實驗 69
第五章 聲子晶體共振腔之聲能能量擷取 82
51 能量擷取壓電模型 82
52 聲子晶體與聲子晶體共振腔實驗 85
53 PVDF壓電薄膜 86
54 聲能能量擷取實驗 87
541 能量擷取效率 87
542 LDT4028k 88
543 LDT2028k 89
第六章 綜合結論與未來展望 100
61 綜合結論 100
62 未來展望 102
參考文獻 103
附錄 116
自述 119

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