臺灣博碩士論文加值系統

傳統的壓電懸臂梁能量採集器末端位移大且應變分佈不均，相較之下，簡支梁則有更佳的應變分佈且端點位移也較小，但其卻有較高之共振頻率。本研究基於簡支梁提出一種延伸式簡支梁壓電能量採集器，在簡支梁上佈滿PVDF壓電片作為主梁，並使用滾軸及轉軸固定兩端點的側向位移，而在轉軸另外一端外加延伸梁和末端質量，透過延伸梁長度和末端質量調整共振頻率。本研究理論模型使用古典梁理論與壓電本構方程式作為基礎，在滾軸及轉軸外加扭力彈簧與主梁施加軸向預力，建立其理論模型，將無外加扭力彈簧與軸向預力的設計作為原型，使用不同延伸梁長度及基底激振加速度以實驗結果驗證，並透過改變理論模型中的扭力彈簧常數與軸向預力大小，討論各參數對延伸式簡支梁性能的影響。實驗結果顯示，在相同共振頻率的條件下，延伸梁長度越短，壓電片最大應變越大。模擬結果顯示，在相同共振頻率與壓電片最大應變一致的條件下，對主梁施加適當軸向預壓力，可以使其應變分佈更均勻。以延伸梁長度20 mm的延伸式簡支梁原型設計與懸臂梁的實驗結果相比，在相同加速度與共振頻率一致的條件下，由於延伸式簡支梁應變分佈較均勻，其輸出電壓較高，末端位移也較小，最大輸出功率可提升約86 %，末端位移可減少約63.2 %。

The conventional piezoelectric cantilever energy harvester has the disadvantages of large transverse displacement and low output voltage due to uneven strain distribution. In contrast, the simply supported beam has more even strain distribution and smaller transverse displacement. However, its resonance frequency is too high so the application is limited. Therefore, this study proposes an extended simply supported beam piezoelectric energy harvester. The proposed design is composed of a main beam and an extended beam. The main beam is a simply supported beam covered with PVDF and clamped by a roller and a pin. The extension beam is attached to the other side of the pin. The resonance frequency can be adjusted by tuning the length of extension beam and the tip mass which is installed at the end of the extension beam. In this study, the motion and circuit equations of the theoretical model is derived based on the Euler-Bernoulli beam theory and piezoelectric constitutive equation. In the theoretical model, torsion springs at the pin and roller and an axial preload are also considered to see their impact on the performance. Base excitation experiment is conducted to verify the theoretical model. In order to analyze the influences of torsion springs and the axial preload, this study performs a simulation by using different spring constants and axial preloads and compares the effects of various parameter changes. The experimental results show that the shorter extension beam brings the greater maximum central stain of PVDF when the resonance frequency is the same. The simulation results show that the strain distribution may be even when the axial pre-stress is applied to the main beam. Compared with the experimental results of cantilever piezoelectric energy harvester, the maximum output power of proposed harvester with extension length of 20 mm is improved by about 86 %, the maximum transverse displacement is decreased by about 63.2 % respectively.

口試委員會審定書 #
誌謝 i
摘要 ii
ABSTRACT iii
目錄 iv
圖目錄 vi
表目錄 viii
符號表 ix
Chapter 1 序論 1
1.1 前言 1
1.2 文獻回顧 2
1.3 研究動機與方法 9
1.4 論文架構 10
Chapter 2 壓電能量採集理論 11
2.1 壓電效應 11
2.2 壓電本構方程式 13
2.3 線性壓電懸臂梁振動能量採集器模型 16
Chapter 3 線性延伸式簡支梁振動能量採集器模型 22
3.1 延伸式簡支梁之振動模型 22
3.2 延伸式簡支梁之電路模型 29
Chapter 4 實驗設計 32
4.1 原型設計 32
4.2 實驗設備 35
4.3 實驗流程 39
Chapter 5 結果驗證與討論 41
5.1 線性壓電懸臂梁驗證 41
5.2 線性延伸式簡支梁驗證 46
5.3 末端質量與延伸長度對於延伸式簡支梁的性能影響 53
5.3.1 末端質量和延伸長度對工作空間的影響 53
5.3.2 末端質量和延伸長度對應變分佈的影響 56
5.3.3 末端質量和延伸長度對輸出電壓的影響 58
5.4 扭力彈簧或軸向預力對於延伸式簡支梁的性能影響 60
5.4.1 在滾軸加入扭力彈簧對性能的影響 61
5.4.2 在轉軸加入扭力彈簧對性能的影響 64
5.4.3 在主梁施加軸向預拉力對性能的影響 67
5.4.4 在主梁施加軸向預壓力對性能的影響 70
5.5 延伸式簡支梁與壓電懸臂梁討論 73
Chapter 6 結論與未來展望 80
6.1 結論 80
6.2 未來展望 81
參考文獻 82
附錄 A 矩陣 之係數 85
附錄 B 矩陣 之行列式展開推導過程 87

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