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研究生:李翔宇
研究生(外文):Xiangyu Li
論文名稱:結合非線性力的旋轉式雙自由度壓電能量採集器分析
論文名稱(外文):Analysis of a Rotational Nonlinear Two-degree-of-freedom Piezoelectric Energy Harvester
指導教授:蘇偉儁
指導教授(外文):Wei-Jiun Su
口試委員:舒貽忠陳蓉珊
口試委員(外文):Yi-Chung ShuJung-San Chen
口試日期:2021-01-25
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:機械工程學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2021
畢業學年度:109
語文別:中文
論文頁數:99
中文關鍵詞:幾何非線性旋轉運動壓電能量收集雙自由度擋板非線性磁力非線性
外文關鍵詞:geometric nonlinearityrotational motionpiezoelectric energy harvestertwo-degree-of-freedomImpact-based nonlinearitymagnetic nonlinearity
DOI:10.6342/NTU202100287
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本論文提出一種用於旋轉環境的雙自由度壓電能量收集器。收集器設計為折返樑結構以獲得低頻下頻率相近的兩個共振頻峰值的效果。模型上本文放寬傳統古典樑假設中的小位移振動的限制,以幾何非線性的模型來探討旋轉環境大位移振動下發電電壓之頻響與頻寬的數值解。研究中首先考慮改變折返樑結構參數對發電效率的影響。特別研究了當上升模態,即共振頻率隨轉速提升而上升的模態,其共振频率先於和後於模態轉向(mode veering)發生的兩種情況下的電壓掃頻結果,並取得接近現實情況的模擬結果。為使系統頻寬拓寬,實驗還使用兩種非線性外力作用:一種藉由機械檔板的碰撞產生非線性脈衝力來改變系統剛性;另一種藉由磁力以非接觸的方式來改變系統的剛性。最後,對比實驗結果與模型數值擬合結果,探討其現象。研究發現,引入非線性力在大部分情況下對雙自由度系統的共振頻寬拓展效果顯著,在一些條件下情況則不夠理想,並且普遍存在發電效率下降的情況。
This thesis proposes a two-degree-of-freedom piezoelectric energy harvester for rotational excitations. The harvester is based on a cut-out beam structure to obtain two close resonant frequencies. In this model, we remote the limitation of small displacement vibration in the traditional classical beam theory, and use a geometric nonlinear model to obtain the numerical results of the frequency response and bandwidth of the generating voltage under large-displacement vibration in a rotating environment. First, we discuss the effect of different structure parameters in energy harvesting efficiency. Besides, we investigate the frequency sweeping results when the resonant frequency of the up mode, which is the case when the resonant frequency increases with the rotation speed, occurs before and after mode veering. The simulation results match the experiment results well. This study uses two types of nonlinear external force to broaden the bandwidth: the mechanical stopper which generates a nonlinear impulse force to change the rigidity of the system by colliding; the magnetic force which changes the rigidity of the system in a non-contact way. Finally, we discuss the phenomenon by compare the experimental results with the simulations. In conclusion, the nonlinear force is effective in bandwidth expanding of our two-degree-of-freedom piezoelectric energy harvester in most situations, while not so well in some other conditions. The decreasing of power generation efficiency is universal.
目錄
誌謝 i
摘要 ii
ABSTRACT iii
目錄 iv
圖目錄 vii
表目錄 x
Chapter 1 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.3 研究動機與方法 8
1.4 論文架構 9
Chapter 2 壓電理論 10
2.1 壓電效應 10
2.2 壓電本構方程式 12
Chapter 3 旋轉壓電折返樑模型 14
3.1 旋轉壓電折返樑力學模型 15
3.1.1 強迫振動方程 15
3.1.2 模態分析 24
3.1.3 正規化處理 27
3.2 旋轉壓電折返樑電學模型 32
3.3 數值計算和模態處理 34
Chapter 4 非線性模型 37
4.1 脈衝非線性模型 38
4.1.1 機械擋模型 38
4.1.2 脈衝模型 39
4.2 磁力非線性模型 44
4.2.1 磁力模型 44
4.2.2 系統模型 46
Chapter 5 實驗設計 49
5.1 原型設計 49
5.2 實驗儀器 52
5.3 實驗流程 55
5.3.1 基底激振實驗 55
5.3.2 旋轉環境實驗 57
Chapter 6 驗證與討論 59
6.1 壓電材料簡化假設 59
6.2 旋轉折返樑模型驗證 62
6.2.1 旋轉折返基樑驗證 62
6.2.2 結構參數調節影響與驗證 65
6.3 擋板非線性模型驗證 74
6.3.1 擋板驗證 74
6.3.2 主樑末端擋板模型驗證 75
6.3.3 副樑末端擋板模型驗證 79
6.4 磁力非線性模型驗證 82
6.4.1 磁鐵模型驗證 82
6.4.2 主樑末端磁力模型驗證 83
6.4.3 副樑末端磁力模型驗證 88
Chapter 7 結論與未來展望 93
7.1 結論 93
7.2 未來展望 94
參考文獻 95
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