具壓電振動子之超穎材料板動態行為分析與應用

Abstract

本研究結合超穎材料的局部共振特性與壓電材料的正壓電效應，設計可將振動能轉換為電能的超穎材料板，預期能提供微型能量擷取器的壓電共振子設計理念。 為探討加入壓電效應對超穎材料局部共振的影響，首先進行理論推導，最後提出具壓電效應的超穎材料板運動方程式。超穎材料板的實際運動分析又可分為有限元素模擬及實驗兩部分，首先透過電腦輔助分析軟體COMSOL進行模擬，設計多個不同特徵頻率之內質量共振單元，並將以上內質量單元利用不同排列順序、不同內質量單元數量等變數組合成具有局部共振特性的超穎材料板，在針對所設計之超穎材料板以結構力學模組分析該模型在承受負載時因結構局部共振所造成的振動現象，同時也利用壓電模組進行壓電輸出的模擬。實驗部分則利用激振器給予固定頻率之負載，針對單一種內質量單元所組成之單共振超穎材料板進行簡諧試驗，最後比較模擬與實驗之結果。 由於原先設計之超穎材料模型振動並未如預期，因此另外提出與原先單共振模型結構差異較大之雙共振及多共振超穎材料模型，再以Comsol的結構力學模組分析其局部共振的效果。 最後本研究成功設計出具有單共振效果、雙共振效果及多共振效果之超穎材料板，但因為所設計超穎材料板厚度略薄，使得本身超穎材料板模態也略在低頻區域，會影響所預期之振動結果。

In this thesis, we combine local resonance characteristics of metamaterials and direct piezoelectric effect of piezoelectric material, design metamaterials sheet which can transform vibration energy into electrical energy. It expects to provide the design concept of the piezoelectric resonator of micro-energy harvesting. To explore the local resonance influence for the metamaterial that add direct piezoelectric effect. First we derivate the theory, then make a motion eqation for Metamaterials plate which have direct piezoelectric effect. The analysis of actual motion can be divided into finite element analysis simulation and experiments in two parts. First we use computer-assisted analysis software “COMSOL” to simulate, design several different characteristic frequencies of resonance mass-in-mass, and use different sort order, different mass-in-mass unit quantity variable of above mass-in-mass unit to combination to have local resonance properties of metamaterials sheet, then base on the metamaterials sheet which we design, use structural mechanics module to analysis when the model under load cause phenomena of Vibration due to local resonance of structure, but also use piezoelectric modules to simulate piezoelectric output. Experimental parts use the loads which is given fixed-frequency by shaker, then base on consisting of a single mass-in-mass unit for a single resonant metamaterials plate to do simple harmonic test. Finally, compare the result for simulation and experimental. Since metamaterials vibration of the original design was not as expected, it also presents double resonance and multiple resonance metamaterials models that are quite different with single resonance metamaterials models, then use Comsol’s solid machanics models analysis the consequent of local resonance. Finally, this study successfully designed metamaterials plates which have single resonance, double resonance and multiple resonance effect, but because of the metamaterials designed itself are too thin, cause metamaterials sheets model type also slightly in the low frequency region , it will affect the vibration of the expected results.