本論文主旨在於透過設計不同型式之邊界連接壓電雙晶片，以降低其共振頻率，本論文所設計的邊界型式有：具有柔度的彈性支架邊界、將試片一端接上彈簧之單邊彈簧邊界以及試片兩端均接上彈簧之雙邊彈簧邊界，本論文將實地製作多種邊界，並透過多種不同之實驗方法進行實驗驗證，實驗之結果將與有限元素法與理論分析之結果進行比較，以確認其準確性，其中理論分析的部分，本研究透過樑理論模型來探討壓電材料之振動特性，透過該模型可探討試片在不同線性勁度與扭轉勁度之邊界下，將對應哪些共振頻率，此外在進行實驗之過程中亦會量測單邊固定與雙邊固定邊界之振動特性，以作為共振頻率降低之比較基礎。本研究透過三種量測設備來協助進行分析，包括全域式的電子斑點干涉術（Electric Speckle Pattern Interferometry，簡稱 ESPI）可針對壓電材料進行即時量測，記錄三維振動的模態振形與共振頻率的參考依據；雷射都卜勒振動儀（Laser Doppler Vibrometer，簡稱 LDV）可針對壓電材料單點的面外（out-of-plane）振動進行穩態掃頻量測位移分析，並且可以獲得壓電材料的面外共振頻率；阻抗分析儀（Impedance Analyzer）則針對壓電材料的電性作量測，可獲得面內振動的共振頻率，同時亦可獲得反共振頻率。由實驗結果發現彈性支架邊界與彈簧邊界均能有效的降低試片共振頻率，但部分邊界設計在降頻的同時會有降低試片輸出電壓之現象，雙邊雙彈簧邊界為本研究中較佳之邊界型式，該邊界型式除了能大幅降低共振頻率外，亦能提高能量擷取時之電壓輸出。此外本研究所推導之理論模型與模擬結果亦有良好之對應性。

In this paper, the purpose of this investigation is to design the different boundary conditions to connect the PZT for reducing its natural frequency. The boundary conditions are including both on elastic fixtures and spring boundaries. The several designs used on a series of experimental measurements to verify our predictions. The experimental results are compared with the FEM and theoretical analysis. The Euler-Bernoulli’s beam theory is used to analyze on the vibration characteristics of piezoelectric materials. The natural frequencies of piezoelectric plates are calculated based on three boundary conditions, i.e., clamped end, linear and torsional stiffness. In addition, the natural frequencies of the clamped-end boundary condition are determined as the basis for comparison with the reduction of the natural frequency.
Three experimental techniques are used to measure the dynamic characteristics of piezoelectric materials. First, the full-field optical technique, amplitude-fluctuatio n electronic speckle pattern interferometry (AF-ESPI), can measure simultaneously the resonant frequencies and mode shapes for out-of-plane and in-plane vibrations. Second, the pointwise measurement system, laser Doppler vibrometer (LDV), can obtain resonant frequencies by dynamic signal swept-sine analysis. Third, the correspondent in-plane resonant frequencies and anti-resonant frequencies are obtained by impedance analysis. It is found that the boundary conditions under the elastic fixtures and the spring boundaries can effectively reduce the resonant frequency of the PZT, However, some of the boundary conditions might reduce the output voltage of the piezoelectric voltage energy harvester at the same time. It can be concluded on that the bilateral spring boundary is the better boundary condition when the PZT was designed both on the lower down frequency and higher the voltage output. It is shown on good agreement between the theoretical analysis, FEM calculation, and experimental measurements in this study.

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