薄膜複合壓電圓板開發近場聲學元件之理論解析、數值計算與實驗量測

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研究生：	陳冠宇 Kuan-Yu Chen
論文名稱：	薄膜複合壓電圓板開發近場聲學元件之理論解析、數值計算與實驗量測 Theoretical Analysis, Numerical Calculation and Experimental Measurement on Membrane Composite Piezoelectric Circular Plate Development Near-Field Acoustic Components
指導教授：	劉孟昆 Meng-Kun Liu 黃育熙 Yu-Hsi Huang
口試委員:	趙振綱 Ching-Kong Chao 黃育熙 Yu-Hsi Huang 劉孟昆 Meng-Kun Liou
學位類別：	碩士 Master
系所名稱：	工程學院 - 機械工程系 Department of Mechanical Engineering
論文出版年：	2019
畢業學年度：	107
語文別：	中文
論文頁數：	272
中文關鍵詞：	薄板理論、壓電陶瓷圓盤、壓電陶瓷圓環、薄膜、聲學元件、振動、聲壓、聲固耦合分析、共振頻率
外文關鍵詞：	acoustic-structure interaction
相關次數：	點閱：361 下載：4
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上一筆

本研究透過理論分析及有限元素數值計算，探討壓電陶瓷圓盤及圓環在單層、雙層並聯型於不同邊界條件下的面外振動特性，以及具有特定張力大小的圓形、環形薄膜於軸向無阻尼自由振動下的特性，接著以理論分析探討並聯型雙層壓電陶瓷圓盤複合環形薄膜結構於不同邊界條件對振動與聲學模型的適用性。使用全域式電子斑點干涉術(Electronic Speckle Pattern Interferometry, ESPI)、雷射都卜勒振動儀(Laser Doppler Vibrometer, LDV)及阻抗分析儀三種實驗技術量測自行切割並黏合之雙層壓電陶瓷的振動特性，並與理論解析、有限元素數值計算進行比較，而針對圓形振膜將使用 ESPI、LDV 進行量測，並透過具阻尼的圓形薄膜之振動理論預估實際薄膜所附有的張力大小。
利用前述的分析方法，本研究設計並聯型雙層壓電陶瓷圓盤複合環形薄膜之近場聲學元件(DA)和並聯型雙層壓電陶瓷圓環複合圓形薄膜之近場聲學元件(AC)，比較兩者的振動特性與聲學響應兩者之間的關係，使用四項測量方法，包括 ESPI、LDV、阻抗分析儀和聲學測量(acoustic measurement, AM)，以及有限元素法所建立聲場模擬計算之方法。針對兩款薄膜複合壓電圓板之近場聲學元件(DA)、(AC)於不同電極連接型式下，以實驗測量方法(ESPI、LDV、Impedance)探討結構振動之特性，另外透過有限元素法於聲場計算與實際聲學測量(AM)的結果進行比較，以佐證有限元素法應用於聲場的計算結果，最後以 ESPI 與 AM 之實驗結果分析其振動和聲學響應之間的關係。本研究綜合理論解析、數值分析與實驗量測，以薄膜複合壓電圓板與圓環設計近場聲學元件的研究方法，可應用於新型揚聲器最佳化聲場增益特性之聲音品質的開發。

This thesis used the theoretical analysis and finite element method(FEM) to investigate the out-of-plane vibration characteristics of piezoelectric ceramic circular and annular plates, which include one-layered piezoelectric disk and two-layered piezoelectric plates under different boundary conditions. As well as, the circular and annular membranes with specific tension are studied on the characteristics of axial undamped free vibration. Then, applied on the several boundary conditions to solve the theoretical solution for the structure of the two-layered piezoelectric ceramic disc compounded with annular membrane. In this study, three experimental techniques are used, including AF-ESPI, LDV, and impedance analyzer, to obtain the vibration characteristics of two-layered piezoelectric ceramics plates. The circular diaphragm is measured using ESPI and LDV, and the membrane theory with damped is used to estimate the tension of the actual membrane. The experimental results are compared and shown good agreement with the FEM and theoretical solutions.
This study investigates also on the vibration characteristics and acoustic response of near-field acoustic components, as well as employed four evaluation methods. The experimental techniques, included on AF-ESPI, LDV, impedance analyzer and acoustic measurement (AM), were employed form 20 Hz to 20 kHz. The experimental measurements are used to obtain the vibration characteristics of near-field acoustic components, which are connected by series and parallel electrically connections. In addition, the sound field calculation in FEM is compared with acoustic measurement (AM) to verify the results in sound pressure level. Finally, the relationship between vibration and acoustic response is discussed by the experimental results of ESPI and AM. This study uses theoretical analysis, finite element numerical calculation and experimental measurements to design near-field acoustic components. This research can be applied to the development in the optimization of sound quality for the novel loudspeaker.

中文摘要 ................................................................................................................... I
Abstract ................................................................................................................... III
誌謝 .......................................................................................................................... V
目錄 ........................................................................................................................ VI
圖目錄 ................................................................................................................... XII
表目錄 ............................................................................................................... XVIII
第一章 緒論............................................................................................................. 1
1 研究動機 ..................................................................................................... 1
2 文獻回顧 ..................................................................................................... 2
3 論文內容簡介 ............................................................................................. 8
第二章 實驗原理、架設與聲學耦合與壓電基本理論 .......................................... 11
1 電子斑點干涉術 ........................................................................................ 11
1.1 面外振動量測 ................................................................................. 13
2 雷射都卜勒振動儀 ................................................................................... 21
3 阻抗分析儀 ............................................................................................... 24
4 奈米壓痕機械性質分析儀 ........................................................................ 28
5 聲學測量(AM) .......................................................................................... 32
6 聲學耦合轉換 ........................................................................................... 34
7 壓電基本理論 ........................................................................................... 36
第三章 元件設計與製作程序 ................................................................................ 40
1 元件的製作方式 ....................................................................................... 40
1.1 振膜的繃膜製程 ............................................................................. 40
1.2 壓電陶瓷的切割、黏合方法.......................................................... 43
2 薄膜的材料常數及量測方法 .................................................................... 46
2.1 薄膜材料常數的量測方法 ............................................................. 46
2.2 薄膜的材料常數 ............................................................................. 48
3 近場聲學元件的設計 ................................................................................ 51
3.1 並聯型雙層壓電陶瓷圓盤複合環形薄膜之近場聲學元件 ........... 51
3.2 並聯型雙層壓電陶瓷圓環複合圓形薄膜之近場聲學元件 ........... 54
第四章 壓電陶瓷圓盤及圓環振動特性分析與實驗量測 ..................................... 58
1 壓電陶瓷振動分析理論推導 .................................................................... 58
2 單層壓電陶瓷振動特性理論分析 ............................................................ 62
2.1 簡介 ................................................................................................ 62
2.2 單層壓電陶瓷應力、電場與位移關係 .......................................... 63
2.3 單層壓電陶瓷圓盤軸向振動特性理論分析 .................................. 65
2.4 單層壓電陶瓷圓環軸向振動特性理論分析 .................................. 70
3 單層壓電陶瓷圓盤及圓環於軸向振動特性理論解析、數值分析與實驗量
測之比較 ......................................................................................................... 75
3.1 簡介 ................................................................................................ 75
3.2 試片規格及 FEM 數值分析設定介紹 ............................................ 76
3.3 單層壓電陶瓷圓盤及圓環軸向振動理論解析與數值分析之比較 77
3.4 單層壓電陶瓷圓盤於自由邊界之軸向振動理論解析、數值分析與
實驗量測之比較 ..................................................................................... 78
4 雙層壓電陶瓷振動特性理論分析 ............................................................ 95
4.1 簡介 ................................................................................................ 95
4.2 雙層壓電陶瓷應力、電場與位移關係 .......................................... 96
4.3 並聯型雙層壓電陶瓷圓盤軸向振動特性理論分析 ....................... 99
4.4 並聯型雙層壓電陶瓷圓環軸向振動特性理論分析 ......................105
5 並聯型雙層壓電陶瓷圓盤及圓環於軸向振動特性理論解析、數值分析與
實驗量測之比較 ............................................................................................ 111
5.1 簡介 ............................................................................................... 111
5.2 試片規格及 FEM 數值分析設定介紹 ............................................. 111
5.3 並聯型雙層壓電陶瓷圓盤及圓環軸向振動理論解析與數值分析之
比較 ........................................................................................................ 112
5.4 並聯型雙層壓電陶瓷圓盤以(串聯、並聯)電極連接方式於軸向振
動實驗量測與理論解析之比較 ............................................................. 113
5.5 並聯型雙層壓電陶瓷圓環以(串聯、並聯)電極連接方式於軸向振
動實驗量測與理論解析之比較 ............................................................. 116
第五章 圓形及環形薄膜振動特性分析與實驗量測 ............................................147
1 薄膜於無阻尼之自由振動理論分析........................................................147
1.1 簡介 ...............................................................................................147
1.2 圓形薄膜的統御方程式(governing equation) ................................148
1.3 圓形、環形薄膜於無阻尼之自由振動理論分析 ..........................151
2 FEM 數值分析方法 ................................................................................154
3 圓形及環形薄膜於無阻尼之自由振動理論解析與數值分析之比較......157
3.1 試片規格及 FEM 數值分析設定介紹 ...........................................157
3.2 圓形及環形薄膜於軸向無阻尼之自由振動理論解析與數值分析之
比較 ........................................................................................................158
4 薄膜具阻尼之振動理論分析 ...................................................................169
4.1 簡介 ...............................................................................................169
4.2 圓形薄膜具阻尼之振動理論分析 .................................................169
4.3 阻抗類比分析 ................................................................................170
5 圓形薄膜具阻尼之振動理論解析與實驗量測之比較 .............................173
5.1 簡介 ...............................................................................................173
5.2 試片規格及實驗架設方式與方法 .................................................173
5.3 圓形薄膜實驗量測及探討 ............................................................173
第六章 並聯型雙層壓電陶瓷圓盤複合環形薄膜之結構振動特性 .....................182
1 各種邊界連接型式的介紹及其特徵方程式 ............................................182
1.1 Model (A)的邊界假設 ...............................................................184
1.2 Model (B)的邊界假設 ................................................................186
1.3 Model (C)的邊界假設 ................................................................188
1.4 Model (D)的邊界假設 ...............................................................190
1.5 Model (E)的邊界假設 ................................................................192
1.6 壓電圓盤假設為剛體邊界 ............................................................193
2 並聯型雙層壓電陶瓷圓盤複合環形薄膜結構之振動特性理論解析與數值
分析之比較 ....................................................................................................195
2.1 試片規格及 FEM 數值分析設定介紹 ...........................................195
2.2 並聯型雙層壓電陶瓷圓盤複合環形薄膜結構於軸向振動特性理論
解析與數值分析之比較 .........................................................................196
第七章 壓電近場聲學元件分析結果與討論........................................................209
1 FEM 數值分析方法 .................................................................................209
2 並聯型雙層壓電圓環複合圓形薄膜以數值分析預估不同尺寸效應下的聲
學響應特性 ....................................................................................................212
2.1 簡介 ...............................................................................................212
2.2 試片規格及 FEM 數值分析設定介紹 ...........................................212
2.3 並聯型雙層壓電圓環複合圓形薄膜以數值分析預估不同尺寸效
應下的聲學響應之比較 .........................................................................214
3 並聯型雙層壓電圓盤於(串聯)電極連接型式附合環形薄膜之近場聲學元
件(DA)於數值分析與實驗量測之比較 .........................................................216
3.1 簡介 ...............................................................................................216
3.2 試片規格及 FEM 數值分析設定介紹 ...........................................216
3.3 實驗結果比較-結構振動 ...............................................................217
3.4 FEM 模擬聲場計算與實際聲學測量(AM)的結果比較 ................218
3.5 ESPI 與 AM 之實驗結果比較 .......................................................219
4 並聯型雙層壓電圓盤於(並聯)電極連接型式附合環形薄膜之近場聲學元
件(DA)於數值分析與實驗量測之比較 .........................................................228
4.1 試片規格及 FEM 數值分析設定介紹 ...........................................228
4.2 實驗結果比較-結構振動 ...............................................................228
4.3 FEM 模擬聲場計算與實際聲學測量(AM)的結果比較 ................229
4.4 ESPI 與 AM 之實驗結果比較 .......................................................230
5 並聯型雙層壓電圓環於(串聯)電極連接型式附合圓形薄膜之近場聲學元
件(AC)於數值分析與實驗量測之比較 .........................................................239
5.1 試片規格及 FEM 數值分析設定介紹 ...........................................239
5.2 實驗結果比較-結構振動 ...............................................................240
5.3 FEM 模擬聲場計算與實際聲學測量(AM)的結果比較 ................241
5.4 ESPI 與 AM 之實驗結果比較 .......................................................241
6 並聯型雙層壓電圓環於(並聯)電極連接型式附合圓形薄膜之近場聲學元
件(AC)於數值分析與實驗量測之比較 .........................................................250
6.1 試片規格及 FEM 數值分析設定介紹 .........................................250
6.2 實驗結果比較-結構振動 ...............................................................250
6.3 FEM 模擬聲場計算與實際聲學測量(AM)的結果比較 ................251
6.4 ESPI 與 AM 之實驗結果比較 .......................................................252
7 近場聲學元件(AC)和(DA)測量結果比較 ...............................................262
第八章 結論與未來展望 ......................................................................................264
1 結論..........................................................................................................264
2 未來展望 ..................................................................................................267
參考文獻 ...............................................................................................................268
                                

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