本研究以一非線性彈性樑為主體，其一端為固定端(Fixed End)，另一端為自由端(Free End)，模擬一裝置於機翼後方、旋翼機主旋翼下方或任何會振動設備後方之彈性鋼片(Single Elastic Steel Sheet(SESS))振動獵能系統，並輔之以另一非線性彈性鋼片附加於非線性彈性鋼片主體上，形成一雙彈性鋼片(Double Elastic Steel Sheet (DESS))振動系統。吾人於此DESS系統之彈性鋼片適當位置裝設壓電片(Piezo-Patch)，以將振動能轉換為電能，形成一動力獵能系統。此獵能系統除了藉由SESS主體上之PZT-Patch振動形變產生電能，並藉由另一片SESS振動並拍擊原SESS主體，再一次利用拍擊發電，與原系統發揮1+1大於2的效益。首先，吾人以牛頓第二運動定律為基礎，並參考Bernoulli-Euler Beam理論模型，推導出此非線性彈性樑之運動方程，並與電能理論推導的壓電方程耦合，再利用時間多尺度法(Method of Multiple Scales (MOMS))將運動方程式分成兩個不同的時間尺度，找出系統各模態振動頻率之比值，並探討是否有內共振之現象，以確定後續分析之彈性樑的模態。此外，為了分析發電效益，吾人利用四階Runge-Kutta法分析此耦合系統，並與實驗量測結果比較，證明此理論模式是可以準確預估實驗結果。最後，吾人以一空氣動力函數模擬機翼的空氣動力流場及其尾流對於本彈性樑系統之阻尼的影響，利用Floquet Theory 搭配 Floquet Multipliers (F.M.)判定法則來分析此系統之穩定性，藉由改變風速的大小，繪製出各風速影響之下的Basin of Attration (BOA)圖形，觀察此系統在不同風速下之穩定性，以獲得最後結論。

This study considers a slender fixed-free nonlinear beam subjected to unsteady aerodynamic forces. We added another single elastic steel sheet (SESS) to the main SESS to instruct a double elastic steel sheet (DESS) vibration system. This DESS system can be installed with a PZT-Patch to simulate a Vibration Energy Harvester(VEH) system attached behind an aircraft wing trailing edge or down stream of a helicopter main rotor. The objective of this study is to convert the vibration energy into electric energy. We applied Newton's second law of motion, and referred the Bernoulli-Euler Beam theoretical model, and coupled with the PZT-Patch equation, we can derive the Vibration Energy Harvester(VEH) of Single Elastic Steel Sheet(SESS). We employed the method of multiple scales (MOMS) to analyze this nonlinear problem.The fixed point plots (steady state frequency response) were obtained. In addition, in order to analyze the electric energy efficiency, we analyze the coupled system by the fourth-order Runge-Kutta method, and compare it with the experimental results to prove that the theoretical model can predict the experimental results. Finally, the wind speeds were included to investigate the stability of this system. The system stability was analyzed by Floquet theory and Floquet multipliers. Then the Floquet Theorem was employed to get the Basin of Attraction of this system and the system stability information was concluded.

目錄
摘要 I
英文摘要 II
目錄 III
表目錄 V
圖目錄 VI
第一章 緒論 1
一、1 研究動機 1
一、2 文獻回顧 1
一、3 研究方法 6
第二章 理論模式之建立與分析 9
二、1 運動方程式之推導 9
二、2 PIEZO-PATCH的理論模式建構 11
二、3 多尺度法 13
第三章 系統內共振之條件 15
三、1 內共振條件之分析 15
三、2 系統之頻率響應分析 17
第四章 單層彈性鋼片與耦合的VEH系統分析 25
第五章 雙彈性鋼片與耦合的VEH系統分析 28
第六章 系統之穩定性分析 31
第七章 結果與討論 34
七、1 附加PIEZO-PATCH系統之內共振分析 34
七、2 單層彈性鋼片與雙層彈性鋼片之發電效益分析 34
七、3 線性與非線性彈性鋼片系統之比較 37
七、4 系統之穩定性分析 41
第八章 結論 43
參考文獻 45
附錄(一) 49
附錄(二) 50
論文簡要版 75

表目錄
表1 單層與雙層彈性鋼片數值模擬與實驗量測之發電效益 51
表2 非線性與線性系統之彈性鋼片數值模擬之發電效益 52

圖目錄
圖1 具壓電片之單層彈性鋼片主體架構示意圖 53
圖2 Fixed-Free Beam Mode Shapes 54
圖3 具壓電片之雙層彈性鋼片主體架構示意圖 55
圖4 激擾第一模態之各模態 Fixed Point圖 56
圖5 激擾第二模態之各模態 Fixed Point圖 57
圖6 激擾第三模態之各模態 Fixed Point圖 58
圖7 附加Piezo-Patch之非線性系統第一模態之位移圖 59
圖8 附加Piezo-Patch之非線性系統第二模態之位移及其局部放大圖	59
圖9 附加Piezo-Patch之非線性系統第三模態之位移及其局部放大圖	60
圖10 附加SESS的Piezo-Patch之非線性系統第一模態之交流電壓圖 61
圖11 附加SESS的Piezo-Patch之非線性系統第二模態之交流電壓及其局部放大圖 61
圖12 附加SESS的Piezo-Patch之非線性系統第三模態之交流電壓及其局部放大圖 62
圖13 附加DESS的Piezo-Patch之非線性系統第一模態之交流電壓圖 62
圖14 附加DESS的Piezo-Patch之非線性系統第二模態之交流電壓及其局部放大圖 63
圖15 附加DESS的Piezo-Patch之非線性系統第三模態之交流電壓及其局部放大圖 63
圖16 附加SESS的Piezo-Patch之非線性系統第一模態之電壓均方根圖	64
圖17 附加SESS的Piezo-Patch之非線性系統第二模態之電壓均方根圖	64
圖18 附加SESS的Piezo-Patch之非線性系統第三模態之電壓均方根圖	65
圖19 附加DESS的Piezo-Patch之非線性系統第一模態之電壓均方根圖	65
圖20 附加DESS的Piezo-Patch之非線性系統第二模態之電壓均方根圖	66
圖21 附加DESS的Piezo-Patch之非線性系統第三模態之電壓均方根圖	66
圖22 附加SESS的Piezo-Patch之線性系統第一模態之交流電壓圖 67
圖23 附加SESS的Piezo-Patch之線性系統第二模態之電壓交流電壓及其局部放大圖 67
圖24 附加SESS的Piezo-Patch之線性系統第三模態之交流電壓及局部放大圖 68
圖25 附加DESS的Piezo-Patch之線性系統第一模態之交流電壓及局部放大圖 68
圖26 附加DESS的Piezo-Patch之線性系統第二模態之交流電壓及局部放大圖 69
圖27 附加DESS的Piezo-Patch之線性系統第三模態之交流電壓及局部放大圖 69
圖28 附加SESS的Piezo-Patch之非線性系統第一模態之電壓均方根圖	70
圖29 附加SESS的Piezo-Patch之非線性系統第二模態之電壓均方根圖	70
圖30 附加SESS的Piezo-Patch之非線性系統第三模態之電壓均方根圖	71
圖31 附加DESS的Piezo-Patch之非線性系統第一模態之電壓均方根圖	71
圖32 附加DESS的Piezo-Patch之非線性系統第二模態之電壓均方根圖	72
圖33 附加DESS的Piezo-Patch之非線性系統第三模態之電壓均方根圖	72
圖34 未附加Piezo-Patch之系統之Basin of Attraction 73
圖35 附加Piezo-Patch之系統之Basin of Attraction 74

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