臺灣博碩士論文加值系統

聲子晶體是以兩種或兩種以上不同材料性質的材料經週期排列而成的結構，可於某頻段產生使彈性波沿任何方向皆無法傳遞的全頻溝(complete band gap)。若將其中一個單胞(unit cell)移除，形成的點缺陷能使彈性波能侷限於其中，經設計使共振頻率位於頻溝，將使點缺陷處成為一共振腔結構。
在壓電振動能量擷取方面，高機械品質因子能提升壓電能量擷取裝置的發電效果，然而高機械品質因子其頻寬較小，自然環境不易激發壓電裝置振動。因此有學者提出以敲擊或是撥動的方式激發壓電能量擷取裝置的振動，而聲子晶體共振腔的高機械品質因子能夠提升其發電功率。
本論文結合板波沿厚度方向限制波傳與局部共振式聲子晶體降低頻溝頻率等優點，設計一柱狀聲子晶體平板。使用有限元素軟體搭配布洛赫理論(Bloch theorem)計算頻散曲線，分析幾何尺寸對頻溝頻率的影響，並設計公分等級的柱狀聲子晶體平板共振腔。經實驗量測，以超聲波黏膠黏貼而成的柱狀聲子晶體平板共振腔，其共振頻率為7.36 kHz與模擬結果相符，其機械品質因子可達652，證實柱狀聲子晶體平板可用來製作點缺陷聲子晶體共振腔。
論文中也以有限元素軟體分析壓電能量擷取裝置於共振腔中之輸出功率，發現壓電層與鋁板存在一最佳厚度比0.3。經實驗量測，共振腔中的壓電能量擷取裝置之機械品質因子為394。研究中，以自製的敲擊機構以每秒8.5次敲擊共振腔中的壓電能量擷取裝置，於外接電阻為10 kΩ時，平均功率為330 μW，相較於沒有聲子晶體共振腔的壓電能量擷取裝置高了15.7倍，證明柱狀聲子晶體平板共振腔能增加發電功率。

Phononic Crystal (PC) is composed of different materials periodically. The complete band gap phenomenon is an important property of the phononic crystal. It is the specific frequency range that wave cannot propagate in such kind of the structure. The defect mode resonant cavity is designed by removed a unit cell in the PC structure.
The piezo energy harvester with the higher mechanical quality factor can harvest more power from the vibration. However, its narrow bandwidth makes the energy harvester hard to match the excited frequency. Therefore, the frequency up conversion technologies like the impact-driven energy harvester device is introduced. And the high mechanical quality factor of the PC resonator can enhance the power harvesting in this device.
In this thesis, the stubbed phononic crystal plate has an advantage of the lowering band gap. In order to understand the coupling between the band gap and the geometry, the dispersion of the phononic crystal is calculated by the finite element method. Then a defect mode phononic crystal resonator is designed completely. The experiment result show that the stubbed phononic crystal plate resonator stuck by hard adhesives has a resonant frequency 7.36 kHz which matches the numerical result. The mechanical quality factor is up to 652, which means that the defect mode resonator can be made of the stubbed phononic crystal plate.
By analyzing the power generated by the piezo energy harvester in the resonator using the finite element method, result shows that the thickness ratio of the piezo layer to Al subtract layer has an optimal value of 0.3. On the other side, the mechanical quality factor of the piezo energy harvester in the PC resonator is 394 in the experiment result. This harvester generates power of 330 μW with an optimal resistance 10 kΩ connected when it is impacted by an impact device driven by a motor with 8.5 strokes per second. The generated power is 15.7 times of the energy harvester without the PC resonator. Results of this thesis show that the resonator cavity of stubbed phononic crystal plate can enhance the generated power.

致謝 I
中文摘要 II
ABSTRACT III
目錄 V
表目錄 VII
圖目錄 VIII
符號對照表 XII
第一章 研究介紹 1
1.1 研究動機 1
1.2 文獻回顧 2
1.3 本文內容 3
第二章 柱狀聲子晶體平板共振腔 7
2.1 聲子晶體波傳理論 7
2.2 設計柱狀共振聲子晶體平板 10
2.2.1 四方排列晶格 10
2.2.2 六方排列晶格 11
2.3 聲子晶體共振腔設計 13
第三章 壓電能量擷取裝置之設計 31
3.1 壓電效應 31
3.2 壓電材料組成律 32
3.3 壓電材料之特性參數 33
3.3.1 力電耦合係數( Electro-Mechanical Coupling Factor ) 33
3.3.2 機械品質因子( Mechanical Quality Factor ) 34
3.3.3 壓電材料選用 34
3.3.4 壓電操作模式 35
3.4 共振腔內能量擷取裝置之功率分析 36
3.5 等效電路模型及電路管理模組 39
3.5.1 等效電路模型 39
3.5.2 LTC-3588電源管理模組 40
3.6 低頻轉高頻之敲擊機制 41
第四章 聲子晶體共振腔與能量擷取之量測 54
4.1 聲子晶體頻溝之量測 54
4.2 以都卜勒雷射量測敲擊純平板之速度訊號 55
4.3 聲子晶體共振腔之特性量測 56
4.3.1 柱狀聲子晶體平板共振腔 57
4.3.2 黏貼壓電陶瓷圓片之柱狀聲子晶體平板共振腔 57
4.4 壓電能量擷取裝置功率輸出之量測 59
4.4.1 敲擊頭對於輸出功率之影響 59
4.4.2 外接電阻對於輸出功率之量測 60
4.4.3 以LTC3588電源管理模組進行能量擷取之量測 61
第五章 結果討論與未來展望 83
5.1 結論 83
5.2 未來展望 84
參考文獻 85

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