Vibration Energy Harvester (VEH) 又稱振動能量收集系統或是振動擷能系統，是一種透過收集振動能並且轉化為電能的系統，本研究利用 VEH 收集雨水落下打擊在遮雨棚時，遮雨棚所產生之振動能，並利用壓電片將收集之振動能轉化為電能。本研究針對非線性板之振動以古典之平板理論 (Classical Plate Theory) 結合 von Kármán-type nonlinearity 計算一邊界條件為 Clamped-Hinged-Free-Hinged 平板之運動方程式，再使用數值分析 Fourth Order Runge-Kutta 計算此平板振動位移。此外，以Ansys模擬軟體，模擬雨滴落下時平板的運動情形，與理論模擬相驗證。針對裝置不同壓電片數量等情況的平板運動模擬，也使用Ansys模擬各個壓電片所可能產生的電壓大小。為貼近真實雨滴落下情況，本研究使用隨機亂數函數作為雨滴落下之力的大小，每一萬個隨機亂數函數，平均作用在平板上。為驗證理論準確性，本研究使用相同隨機亂數函數分別作為理論分析以及Ansys模擬之作用力，同時計算平板運動並記錄其振幅及電壓輸出。
本研究同時以實驗，驗證理論以及模擬之準確性及本設計之可行性。本研究設計實驗平台，以及使用鋼珠及設計機械裝置模擬雨滴隨機衝擊，結果顯示，理論、模擬與實驗所得之最大振幅誤差小於3%，發電電壓亦呈現一致性。此外，實驗中發現拍擊力（impact force）會直接作用於壓電片，提升其發電效能，因此本研究對於理論模型加入拍擊力修正，修正後的理論模型可更貼近實驗結果，顯示本修正模式之可行性。
綜上所述，本研究成功驗證以 VEH 系統收集雨滴落下衝擊平板所產生之振動能，並透過壓電片轉化為電能之可行性，進一步研究發現，若多片壓電片同時承受由雨滴衝擊產生之拍擊力與平板振動所產生之形變，能進一步提升能源轉換效率。本研究所提出之架構具備良好之應用潛力，未來若能進一步優化結構設計與材料配置，將有助於提升系統效能，對綠色能源技術具有發展價值。

This study presents a vibration energy harvester (VEH) system that converts vibrational energy generated by raindrop impacts on a rooftop panel into electrical energy using piezoelectric patches. The dynamic behavior of a nonlinear plate with Clamped-Hinged-Free-Hinged (C-H-F-H) boundary conditions is modeled using Classical Plate Theory integrated with von Kármán-type nonlinearity. The fourth-order Runge-Kutta numerical method is employed to solve the plate’s displacement and predict voltage output. Ansys finite element simulations are also conducted to validate the theoretical model and investigate the influence of varying numbers of piezoelectric patches. To better simulate real rainfall, random force functions are applied to represent raindrop impacts. The same random input is used in both theoretical calculations and Ansys simulations to ensure consistency.
An experimental setup is constructed using a platform with free-falling steel balls to replicate random raindrop impacts. Laser displacement sensors and an imc data acquisition system are used to measure vibration amplitude and voltage output from three piezoelectric patches. The results show that the maximum displacement error between simulation and experiment is less than 3%, indicating high accuracy of the theoretical model. Additionally, the impact force directly acting on the piezoelectric patch is found to enhance voltage generation. After incorporating this impact effect into the theoretical model, the predicted output voltage closely matches experimental data.
In conclusion, this research confirms the feasibility of using VEH systems to harvest vibrational energy from raindrops and convert it into usable electricity. The findings also highlight that applying multiple piezoelectric patches subjected to both impact and structural deformation can significantly improve energy conversion efficiency, providing promising potential for future green energy technologies.

目錄
摘要	I
英文摘要	II
目錄	III
表目錄	IV
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	10
第二章	理論模型之建立與分析	13
二、1.理論模型之建立	13
二、2.非線性平板運動方程式推導	14
二、2.理論模型之數值分析	17
二、3.隨機亂數外力激擾分析	20
二、4.平板受外力激擾之振幅分析	21
二、5. Ansys軟體之振幅模擬	22
二、6.理論與模擬之振幅比較	24
第三章	壓電方程式推導及發電分析	25
三、1.壓電方程式推導	25
三、2.理論發電電量分析	27
三、3. Ansys模擬發電電量分析	29
三、4.理論與模擬之發電電壓比較	31
第四章	實驗設計及分析	33
四、1.實驗裝置設計	33
四、2.實驗系統之振幅及電壓量測	39
四、3.理論、模擬及實驗結果分析	41
第五章	結論	48
參考文獻	50

 
表目錄
表 1 無因次化理論與模擬最大振幅數值	24
表 2 理論與模擬電壓數值	32
表 3 理論、模擬與實驗振幅數值	42
表 4 理論、模擬與實驗發電電壓	42
表 5 有拍擊力之理論電壓及實驗電壓比較	46
表 6 理論、模擬與實驗壓個別壓電片發電電壓比較	47

 

圖目錄
圖 1 Clamped-Hinge-Free-Hinge 邊界條件平板示意圖	13
圖 2 平板受隨機外力激擾示意圖	13
圖 3 平版面內拉伸及剪切示意圖	16
圖 4 為平板受外力激擾10秒所產生之振幅	22
圖 5 二維X-Z平面側視圖	22
圖 6 電腦軟體模擬平板受外力激擾之振幅圖	24
圖 7 三片壓電片放置位置示意圖	27
圖 8 Clamped 邊上之壓電片(G1)之電壓圖	28
圖 9 Hinged 邊上(y=0)之壓電片(G2)之電壓圖	28
圖 10 Hinged 邊上(y=1)之壓電片(G3)之電壓圖	29
圖 11 電腦軟體模型示意圖	30
圖 12 含壓電片平板之第一模態	31
圖 13 實驗架構示意圖	35
圖 14 測試台示意圖	36
圖 15 測試主體示意圖	36
圖 16 實體實驗架構	37
圖 17 Hinge 邊之轉軸	37
圖 18 測試主體(a)正面(b)背面	38
圖 19 機械裝置	38
圖 20 機械裝置(背面)	38
圖 21 間歇驅動圓盤以及內縮圓柱	39
圖 22 間歇驅動圓盤的半齒輪	39
圖 23 imc 資料處理器	39
圖 24 壓電片(G1)實驗發電電壓	40
圖 25 壓電片(G2)實驗發電電壓	41
圖 26 壓電片(G3)實驗發電電壓	41
圖 27 Clamped 邊上之壓電片(G1)拍擊力修正之電壓圖	44
圖 28 Hinged 邊上(y=0)之壓電片(G2)拍擊力修正之電壓圖	45
圖 29 Hinged 邊上(y=1)之壓電片(G3) 拍擊力修正之電壓圖	45
 

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