臺灣博碩士論文加值系統

近年來，利用壓電材料設計振動元，藉由將環境或是因為機器運作產生的振動使振動元可以將振動能量轉換為電能的相關研究愈來愈多，其中一領域就是利用滿足Duffing equation描述的非線性雙穩態系統。利用此系統因為非線性剛性的特點，使系統具有一個不穩定平衡點與兩個穩定平衡點。在環境激發振幅與激發頻率互相配合下，可以產生跨兩個穩定平衡點的大幅度振動，稱之為“Snap-through”現象。而本研究藉由實驗驗證的方式，探討輸入振幅、輸入頻率與磁力大小三者，對非線性雙穩態系統能否進入Snap-through現象的對應關係，以及進入Snap-through現象後的獵能效果與純線性系統之比較。

Bi-stable oscillator is one of the nonlinear vibration structures. The mechanical energy from the environment vibrations or vibrating machines can be transformed to electric energy through the mechanism of piezoelectric energy harvesting. To improve the performance of the energy harvesting, the nonlinear bi-stable oscillation system was investigated by using the Duffing equation. The nonlinear bi-stable oscillation system has one unstable and two stable equilibrium points. When the bi-stable system is excited with certain amplitude and frequencies of inputs, the system presents a bi-stable behavior, called “Snap-through” phenomenon. The oscillator with “Snap-through” phenomenon can produce a larger vibration amplitude and thus induce the piezoelectric materials to generate more electric energy than the pure linear mono-stable system. The purpose of this research is to experimentally validate the conditions of Snap-through phenomenon related to the input amplitude, input frequencies and magnet force. The performance of energy harvesting was also evaluated in case of nonlinear bi-stable system with compared to the pure linear oscillation system.

致謝 i
摘要 ii
Abstract iii
目錄 iv
圖目錄 vii
表目錄 xii
1. 前言 1
1.1. 研究動機 1
1.2. 文獻回顧 2
1.3. 問題討論與研究貢獻 6
1.4. 論文大綱 7
2. 理論 8
2.1. Duffing equation 8
2.2. 系統模型 11
2.3. 壓電材料 13
2.4. 磁力模型 17
2.5. 壓電懸臂樑模型 19
2.5.1. 等效剛性keq 19
2.5.2. 等效質量meq 22
2.5.3. 阻尼c 23
2.5.4. 位移轉換常數Dchange 23
2.6. 實驗數據處理與分析 24
2.6.1. 實驗數據處理 24
2.6.2. 經驗模態分解(EMD分解) 26
2.6.3. 數據處理流程 28
3. 實驗設備及介紹 31
3.1. 實驗架構與流程說明 31
3.2. 實驗平台 32
3.3. 實驗設備介紹 33
3.3.1. 激振器-Model2075E 34
3.3.2. 振動主結構 35
3.3.3. 微型單軸加速規 36
3.3.4. 單軸加速規 37
3.3.5. 電磁鐵 38
3.3.6. 壓電振動片 39
3.3.7. 永久磁鐵夾具及永久磁鐵 42
3.3.8. 線性滑軌 44
3.3.9. 訊號放大器 45
3.3.10. 資料擷取模組 46
3.3.11. 電磁鐵整流器 49
4. 實驗結果與討論 50
4.1. 實驗一:壓電振動系統有無磁力之非線性行為影響 50
4.2. 實驗二:壓電雙穩態振動系統之頻率響應 57
4.3. 實驗三:壓電雙穩態振動系統於輸入振幅之影響 70
4.4. 實驗四:壓電雙穩態振動系統磁距之影響 81
4.5. 實驗五:非線性系統的不穩定區域 84
5. 結論與未來展望 88
5.1. 結論 88
5.2. 未來展望 90
參考資料 91

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