本研究針對歐拉-伯努力樑受軸向簡諧力和非線性拉伸效應的影響討論，並置入壓電材料，討論其壓電耦合之效應。本文探討在橫樑軸向施力，而非在側向施力，從而改變樑之固有頻率。
本研究的目的是為了避免該系統內部共振並且有效控制系統振動。本系統由Mathieu方程控制，端點之致動器外力將影響整個系統的穩定性。因此本文將探討其振動情形與致動器之振幅及頻率對於系統穩定性之影響並利用附加之壓電材料(Piezoelectric material)擷取振動轉換電能。
首先利用牛頓定律推導其運動方程，接著採用多尺度法(Method of Multiple Scales(MOMS)) 分析系統於穩態固定點(Fixed Point Plot)時各模態之頻率響應，並藉由振幅觀察其振動現象。
本文利用實驗測量來驗證理論結果，驗證項目包括不同振動模態(mode)之頻率、振幅，並且置入壓電材料，將用以量測本研究實測之電壓電流等數據，並且最後與理論值相互比對，檢驗實驗與理論是否吻合。
本研究之模式可藉由調整致動器 (Actuator) 之振幅大小及頻率或相位，以達到控制橫樑振動之振幅及穩定性，可用於一般振動主體之振動控制，亦可適用於振動能量 (Vibration Energy) 與電能 (Electric Power Generator) 之間之轉換，應用範圍廣泛。

This study investigates a slender hinged-roller nonlinear Euler-Bernoulli Beam subjected to a simple harmonic force applied in the axial direction. This nonlinear beam considered the stretching effect and also attached with a piezoelectric-patch (PZT-patch) to transfer nonlinear vibration energy into the electric power. Instead of applying the force on the beam’s transversal direction, the present work applies an axial force (an axial actuator) on the longitudinal direction to change the natural frequency of the beam (as shown in Fig.1) and hence control the beam vibration to achieve a maximum vibration energy harvesting. 
The actuator's external force amplitude could also affect the stability of the entire system. Therefore, stability analysis will be studied to ensure the energy reliability of this vibration energy harvester (VEH) system. We employed the Method of Multiple Scales (MOMS) to analyse this nonlinear system. The Fixed-Point plots (steady state frequency response) were obtained and compared with the numerical results to verify if the internal resonance existed in this system. 
The VEH system's stability information was obtained by the input-output amplitude plot. The proposed model can be used to adjust the amplitude or frequency of the actuator to control the beam's vibration amplitude and hence to have the maximum vibration energy transferring effect. 
A simple experiment was performed (see Fig.2) to verify the analytical and numerical results. The output voltage of this VEH system from the present model agrees with experimental results very well. Our proposed model shows a wide application on energy engineering problems.

目錄
目錄	III
圖目錄	V
第一章	緒論	1
一、1 研究動機	1
一、2 文獻回顧	3
一、3 研究方法	12
第二章	理論模式之建立	14
二、1	非線性運動方程式之推導	14
二、2	非線性運動方程式之無因次化	16
二、3	壓電片的理論模型建構	16
二、4	多尺度法(METHOD OF MULTIPLE SCALES，MOMS)	17
第三章	內共振條件分析	20
三、1	系統內共振條件之分析	20
三、2	系統之內共振分析	26
三、3	系統之頻率響應	27
三、4	橫樑與端點致動器系統之穩定性分析	34
第四章	端點鉸接滾軸樑與耦合的VEH系統分析	37
四、1	線性動態方程	37
四、2	非線性動態方程	38
第五章	實驗設置	42
五、1	實驗儀器	42
五、2	實驗測量	44
第六章	結果與討論	47
六、1	附加壓電片後系統之內共振分析結果	47
六、2	橫樑與端點致動器系統之穩定性分析結果	48
六、3	非線性鉸接滾軸樑與線性鉸接滾軸與實驗值之比較	50
六、4	鉸接滾軸之位移以及能量獲取效益討論	50
第七章	結論	53
參考文獻	55
附錄(一) 無因次化參數定義	59
附錄(二) 附表	60
附錄(三) 附圖	62
 
表與圖目錄
表 1 FIXED POINT PLOT 比較表	60
表 2 致動器外力與振幅比較表	60
表 3 理論與實驗位移比較表	61
表 4 理論與實驗伏特比較表	61
圖 1 HINGED-ROLLER BEAM 加裝端點致動器(ACTUATOR)	62
圖 2  激擾第一個模態的第一、二、三模態之 FIXED POINT 圖	63
圖 3  激擾第二個模態的第一、二、三模態之 FIXED POINT 圖	64
圖 4  激擾第三個模態的第一、二、三模態之 FIXED POINT 圖	65
圖 5  致動器 (ACTUATOR) 與橫樑第一模態之振幅響應圖	66
圖 6  致動器 (ACTUATOR) 與橫樑第二模態之振幅響應圖	66
圖 7  致動器 (ACTUATOR) 與橫樑第三模態之振幅響應圖	67
圖 8  激擾第一模態之線性位移-時間響應圖	67
圖 9  激擾第一模態之線性伏特-時間響應圖	68
圖 10  激擾第二模態之線性位移-時間響應圖	68
圖 11  激擾第二模態之線性伏特-時間響應圖	69
圖 12  激擾第三模態之線性位移-時間響應圖	69
圖 13  激擾第三模態之線性伏特-時間響應圖	70
圖 14  激擾第一模態之位移-時間響應圖	70
圖 15  激擾第一模態之伏特-時間響應圖	71
圖 16  激擾第二模態之位移-時間響應圖	71
圖 17  激擾第二模態之伏特-時間響應圖	72
圖 18  激擾第三模態之位移-時間響應圖	72
圖 19  激擾第三模態之伏特-時間響應圖	73
圖 20  壓電材料放置1/10處之伏特隨時間變化圖	73
圖 21  壓電材料放置1/4處之伏特隨時間變化圖	74
圖 22  壓電材料放置1/2處之伏特隨時間變化圖	74
圖 23   實驗儀器設計與製造流程圖	75
圖 24   實驗步驟流程圖	76
圖 25實驗之模擬圖	77
圖 26模擬圖側視圖	77
圖 27模擬圖上視圖	77
圖 28模擬圖部件之固定式底座	78
圖 29長螺絲	79
圖 30樑夾	80
圖 31滑動式底座	81
圖 32實驗設置	82
圖 33實驗致動器位置	82
圖 34訊號產生器	82
圖 35訊號放大器	83
圖 36集研公司所製造的IMC資料收集器	83
圖 37 雷射位移計	84
圖 38 壓電材料	84
圖 39 壓電材料附於彈性樑上	84
圖 40 利用加速規量測得出樑之自然動頻率圖	85
圖 41 激擾第一模態之實驗位移-時間響應圖	85
圖 42 激擾第二模態之實驗位移-時間響應圖	86
圖 43 激擾第三模態之實驗位移-時間響應圖	86
圖 44 激擾第一模態輸入2V之實驗位移-時間響應圖	87
圖 45 激擾第一模態輸入3V之實驗位移-時間響應圖	87
圖 46 激擾第一模態輸入4V之實驗位移-時間響應圖	88
圖 47 激擾第一模態之實驗伏特-時間響應圖	88
圖 48 激擾第一模態之實驗伏特-時間均方根圖	89
圖 49 激擾第二模態之實驗伏特-時間響應圖	89
圖 50 激擾第二模態之實驗伏特-時間均方根圖	90
圖 51 激擾第三模態之實驗伏特-時間響應圖	90
圖 52 激擾第三模態之實驗伏特-時間均方根圖	91

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