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系統識別號 U0026-2209201015464400
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) Liang-Yu 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 two-dimensional 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
1-1 前言 1
1-2 研究動機 1
1-3 文獻回顧 3
1-3-1 基本的聲子晶體 3
1-3-2 含缺陷聲子晶體 7
1-3-3 聲子晶體異常折射 8
1-3-4 能量擷取 10
1-4 本文架構 12
第二章 數值方法 15
2-1固態物理學基本定義 15
2-1-1倒晶格空間 15
2-1-2布里淵區(Brillouin Zones) 17
2-1-3布洛赫定理(Bloch theorem) 19
2-2平面波展開法 19
2-2-1正方晶格排列 22
2-2-2三角晶格排列 23
2-2-3 超晶胞法 24
2-3 有限元素法 25
第三章 聲子晶體共振腔 36
3-1 完美聲子晶體與含點缺陷聲子晶體 36
3-1-1 頻散曲線 36
3-1-2 穿透頻譜 37
3-2 聲子晶體共振腔 39
3-2-1 頻散曲線 39
3-2-2 共振腔壓力場模擬 40
3-3 聲子晶體共振腔實驗 41
3-3-1 聲子晶體之穿透頻譜 41
3-3-2 聲子晶體共振腔中心壓力量測 42
3-3-3 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
4-1頻散曲線 65
4-2 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
5-1 能量擷取壓電模型 82
5-2 聲子晶體與聲子晶體共振腔實驗 85
5-3 PVDF壓電薄膜 86
5-4 聲能能量擷取實驗 87
5-4-1 能量擷取效率 87
5-4-2 LDT4-028k 88
5-4-3 LDT2-028k 89
第六章 綜合結論與未來展望 100
6-1 綜合結論 100
6-2 未來展望 102
參考文獻 103
附錄 116
自述 119
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