以有限元素法探討壓電振動能量擷取系統之機電行為

Abstract

近年來，由於石化能源日近枯竭，使得替代能源的研究議題得到廣泛的討論，在眾多存在於大自然中的能源中，最不受外界影響且生活環境中隨手可得的非「振動能」莫屬。然而隨著微製程與技術的進步，系統所需之功率逐漸降低，因此將外在振動能量擷取轉換成可利用之電能已經得以實現，相關研究也變成一相當重要之議題。 本論文利用力平衡原理與壓電統御方程式建立數學模型及以有限元素法建立完整數值模擬，同時輔以實驗驗證，對壓電振動能量擷取系統進行完整分析。數值模擬部分主要探討壓電懸臂樑在標準介面下之頻率響應。因以有限元素法並無法直接求得標準介面下之頻率響應，在此我們提出一「等效阻抗」分析方法，將標準介面電路化簡成一等效阻抗，並建立壓電懸臂樑之等效電路模型，近似得到等效電路參數，與「等效阻抗」分析結合來求得壓電懸臂樑在標準介面下位移、輸出電壓與輸出功率之頻率響應。論文中除建立分析模式外，更探討壓電懸臂樑長度及厚度等幾何形狀參數對其輸出的影響，透過理論、數值模擬及實驗三種分析方法所得到之結果具備相當高的一致性，可作為壓電振動能量擷取系統的重要參考。

The research of energy harvesting from environmental resources has received increasing attention due to the decreasing supply of fossil energy. With the advances of MEMS technology and the reduction of power requirement in electronic devices, harvesting energy from vibration sources becomes achievable. This thesis studies the vibration-based piezoelectric energy harvesting based on the finite element simulation. First, the mathematical model is established using the force balance principle and the piezoelectric governing equations. Second, the finite simulation is validated by a series of experiment. The main result is the investigation of the frequency response of the piezoelectric cantilever beam endowed with the standard interface. As the current commercial finite element codes are not able to be integrated with the circuit simulators, we propose an “Equivalent Impedance” method to resolve this difficulty. The results are consistent with the theoretical predictions and agree well with experimental observations. The effect of geometry of cantilever configurations on harvested power is also studied.