分佈式壓電片於平板上之能量擷取研究

Abstract

本論文研究旨在探討分佈式壓電片於四邊固定之平板上給予一簡諧力並搭配標準能量擷取電路，並且在不同模態下利用開關切換來控制電路連接，使其達到較高的輸出功率。方法上是藉由平板的邊界條件得知其應變分佈，但由於在高模態下，會產生應變節點之區域，因此壓電片的位置將會受到限制，不當之位置將會有電荷抵消之問題，使其輸出功率降低，故本研究將透過改變壓電片位置，得知其在不同模態下應變節點區域對於標準電路之輸出功率所造成的影響。首先，利用分佈參數法以及板殼理論進行推導壓電系統之力電耦合統御方程式，並使用本研究團隊舒貽忠教授所提出之等效阻抗法，以及用於陣列式能量擷取系統之廣義歐姆定律的矩陣形式，在此將其應用於多模態之矩陣形式，以推導出分佈式壓電片於平板上之結構搭配標準電路的數學理論解。接著，使用有限元素軟體進行模擬驗證。結果顯示，若壓電片位於含有應變節點之區域時，會造成等效力電耦合係數降低，此時，將其並聯至後端標準電路反而會使輸出功率降低，發生使用較少片壓電片之輸出功率高於使用較多片壓電片之情形，因此探討在固定面積下壓電片分佈對多模態能量擷取的重要性。

This thesis investigates the electric response of a plate with multiple piezoelectric patches attached to the standard energy harvesting circuit. These patches are connected electrically by switches for achieving the higher power output when a time varying harmonic concentrated load is applied to the plate whose edges are fixed. The methodology is based on solving the modal formulation of the plate to obtain the distribution of strain nodes. The locations of the piezoelectric patches over the strain nodes will reduce the power output. Therefore, the purpose of the present thesis is to study the multi-frequency energy harvesting by the investigation of the effect of the locations of the piezoelectric patches on the output power. Precisely, the theoretical formulations are derived by applying the parametric distribution method and the plate theory. The analytic estimate of the output power is realized by applying the equivalent impedance approach of the piezoelectric array attached to the standard interface. Next, the theoretical results are validated by COMSOL simulations. The results show that if the locations of the piezoelectric patches occupy parts of the strain nodes, the equivalent piezoelectric coefficients will be decreased, causing the output power smaller than that with fewer number of patches. Thus, it demonstrates the importance of the topology of piezoelectric patches on harvested power under the constraint of the fixed area.