本論文所用的超穎結構模型，為在主樑的左右兩側週期性排列懸臂樑型態的局部共振器，並研究其減振能隙範圍。首先透過哈密頓原理推算頻散曲線能隙位置，以及對應等效質量中發生負質量效應的位置與範圍，可以發現能隙與負質量效應兩者的位置與範圍相符。而後利用有限元素軟體COMSOL運算與繪製頻散關係曲線圖及等效質量圖，並與理論所計算繪製出的頻散曲線作比較，可以發現兩者的結果相符合。後改變局部共振器的參數，研究其對於減振能隙的影響。並進行結合兩種不同參數局部共振器，組合為雙共振器從而增加結構的減振頻帶。最後將壓電材料與超穎結構樑結合，壓電片貼附於局部共振器上，用理論與模擬預測壓電片產生的電壓與功率，可以發現無論理論與模擬之電壓峰值皆發生於頻散曲線能隙的起始位置，雖然理論以及模擬的電阻與功率的關係圖中，最大功率發生之電阻值稍有不同但趨勢相近。

This thesis investigated flexural wave propagation of a metamaterial beam with a pair of sub-beams acting as resonators. Each sub-beam consists of a cantilever beam with tip mass. Due to the local resonance of the sub-beam resonator, a locally resonant band gap is generated. The frequency of band gap can be tuned by altering the length and thickness of cantilever beam or the magnitude of tip mass. Euler beam theory and Hamilton’s Principle are used to derive the equation of motion of the present beam. This thesis also adopts a commercial finite element software (COMSOL Multiphysics) to simulate the dispersion relation of the metamaterial beam. Also, the energy harvesting capability of the metamaterial is evaluated. The piezoelectric films, PVDF, are attached to the sub-beam resonators. It is found that the generated voltage would be the maximum at the initial frequency of band gap.

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