臺灣博碩士論文加值系統

本論文主要可分為兩大部分，第一是為利用有限元素法分析多種量測系統等效參數的方法及其優劣性與準確度。第二是則是針對搭配整流電路的壓電振動試樣之有限元素模型並進行實驗之驗證。
第一部分：利用有限元素法建立出一個壓電振動模型，以此模型透過三種不同方法所得到的系統等效參數之輸出功率結果做討論。此三種方法分別為1.純能量法解法、2.有限元素數值模擬搭配能量法解法、3.等效電路解法。純能量法透過漢米爾頓定理與瑞利-里茲逼近法來求得系統等效參數，在中強力電耦合有不錯的精確度，但在材料參數不完整或是模型具有其他幾何形狀時將導致模態函數不易求得，純能量法將不適用。有限元素數值模擬搭配能量法在強中弱力電耦合皆具有優良的精準度，但此方法需要搭配一部分純能量法解法之公式。最後，等效電路解法在強中弱力電耦合情況皆具有優良的精準度，但此方法僅能求出壓電振動系統中的電學結果，無法得到力學方面的結果。
第二部分：利用壓電振動子試樣，將壓電振動材料參數輸入於有限元素法後建立出具有整流電路之有限元素模型並實際操作壓電振動懸臂樑之實驗結果相互驗證。而實驗當中的壓電振動懸臂樑試樣的後端介面電路包含了交流電路、標準整流電路、並聯式之同步切換開關電感整流電路(Parallel Synchronized Switch Harvesting on Inductor,P-SSHI)三種。最後得到其實驗結果與有限元素軟體之數值模擬解結果吻合且趨勢一致。

This thesis discusses some problems in piezoelectric energy harvesting based on certain finite element (FE) models. It consists of two parts. The first part uses the FE simulation for performance evaluation of different methods used for deriving the equivalent parameters of a piezoelectric energy harvesting system. The second part is to perform the experiment for validating the FE model of a rectified piezoelectric energy harvesting system.

Specifically, there are three methods for finding the equivalent system parameters. The first one is based on the Hamiltonian energy principle and the Rayleigh-Ritz approximation. While all the parameters can be derived analytically, they can only be evaluated if the material properties of a device are known in advanced. In addition, the modal function used in Rayleigh-Ritz approximation may not be available for the case of irregular geometry of piezoelectric elements. The second one is based on the finite element simulation of a piezoelectric system together with the prescribed equivalent mass and force parameters derived from the energy formulation. This approach shows good accuracy, but it needs some parameters from the energy approach. Finally, the third approach is based on the equivalent circuit model. It shows very good accuracy in various magnitudes of electromechanical couplings. However, only the electric parameters can be revealed from this approach.

The second part is to develop an experiment setting for validating the FE model of a rectified piezoelectric energy harvesting system proposed by Prof. Shu’s research group. A piezoelectric cantilevered bimorph is used and the interface circuits include the AC circuit, the standard rectified interface and the parallel synchronized switch harvesting on inductor (P-SSHI) circuit. The experimental results agree quite well with the proposed finite element simulations.

誌謝..............................................................................i
摘要..............................................................................ii
Abstract..........................................................................iii
目錄..............................................................................iv
圖目錄............................................................................vi
表目錄............................................................................x
第一章導論........................................................................1
1.1研究動機..................................................................1
1.2文獻回顧..................................................................2
1.3論文架構..................................................................4
第二章壓電理論....................................................................6
2.1壓電效應..................................................................6
2.1.1正壓電效應...........................................................6
2.1.2逆壓電效應...........................................................7
2.2 線性壓電材料之本構方程式..................................................8
2.3 壓電懸臂樑之數學模型與幾何關係...........................................11
2.4 壓電懸臂樑之等效電路模型.................................................14
第三章 壓電振動系統之等效參數與有限元素模型建立與數值分析........................19
3.1 壓電振動懸臂樑之共振頻率分析.............................................20
3.2 COMSOL數值模擬解法.......................................................22
3.3 純能量法之法.............................................................23
3.4壓電懸臂樑之等效電路參數分析..............................................24
3.5 COMSOL 數值模擬搭配能量法之解法..........................................26
3.6 等效電路之解法...........................................................27
第四章 應用於整流壓電振動系統之有限元素模型建立與數值分析........................29
4.1節 單根壓電振動子在有限元素法中的整流電路等效化..........................29
第五章 不同系統等效參數求法在強中弱力電耦合之數值評估............................33
5.1有限元素法軟體COMSOL的PDE自建模組與壓電振動模組之比較..................33
5.2 強力電耦合壓電振動子在交流電路下之不同解法之分析........................34
5.3 中力電耦合壓電振動子在交流電路下之不同解法之分析........................39
5.4 弱力電耦合壓電振動子在交流電路下之不同解法之分析........................44
第六章 整流壓電振動實驗與有限元素法之結果驗證...................................54
6.1.1實驗架構..............................................................54
6.1.2實驗儀器..............................................................56
6.1.3實驗步驟..............................................................61
6.2實驗結果與數值解結果....................................................63
第七章 結論與展望................................................................69
7.1結論.....................................................................69
7.2未來展望.................................................................71
參考文獻.........................................................................72
附錄A............................................................................75
附錄B.1 COMSOL 材料參數設定......................................................78
附錄B.2壓電懸臂樑之共振頻率分析COMSOL 邊界設定..................................81
附錄B.3壓電懸臂樑之等效電路參數分析COMSOL邊界設定..............................82
附錄B.4壓電懸臂樑交流發電之COMSOL邊界設定......................................83
附錄C.COMSOL各實例操作步驟......................................................86
附錄D 數值模擬軟體COMSOL 3.5a 補充說明..........................................97
附錄E 強力電耦合與中力電耦合增加細長比之誤差結果................................103

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