超材料是一種為了滿足特定需求所加工出來的人造材料，透過微結構精心的幾何設計與性能來加以調控，使材料能夠表現出奇特有趣的物理現象例如負折射率，隱形斗篷或剪力模數遠小於體積模數的五模超材料，而本論文藉由簡單的改變圓形內含物超材料的幾何或位置成為橢圓超材料與偏心圓超材料，並討論其頻散曲線完整路徑的變化，接著經由有限元素軟體的頻域分析搭配複合材料等效理論，計算材料整體的等效質量密度、等效轉動慣量以及等效材料係數，探討不同形式的共振消能機制和材料的雙負性質，並與實際尺度超材料模型之頻域模擬結果相互比對，而後期望能夠有進一步的全域模擬，分析地震波通過超材料的減振、折射、繞射等的現象，亦或是橢圓的交叉排列形式可能將產生更大的帶隙區間。
另外為延伸粽子超材料的研究，利用平面波展開法以及全域模擬的方式來加以驗證頻散曲線的正確性與合理性，說明粽子超材料確實能夠擁有超寬的帶隙區間。由於粽子的特殊結構，因此當受波傳激振時將導致結構體的偏心扭轉，透過此想法我們計算了粽子超材料的等效轉動慣量，並且證實了在超寬帶隙區間裡粽子主要由旋轉共振的行為進行波傳能量的衰減。

Metamaterial is a kind of man-made material processed to meet specific needs. It can be regulated through the careful geometric design and performance of the microstucture, so that the material can exhibit strange and interesting physical phenomena such as negative refractive index, or near zero effective shear modulus. In this thesis we consider an elliptical metamaterial and an eccentric circle metamaterial. Then, we utilize the homogenization theory of composite materials to caculate the effective mass density, moment of inertia and material coefficient, and discuss different forms of resonance energy dissipation mechanisms. In addition, in order to extend the research to Zongzi metamaterials, the correctness of the dispersion curves are verified by plane wave expansion method (PWE) and transmission(dB) simulation, which shows that Zongzi metamaterials can indeed have a wide band-gap. Due to the special structure of the Zongzi, the torsion mode will be induced when vibration is transmitted by the wave. Base on this idea, we calculated the effective moment of inertia of the Zongzi metamaterial, and confirmed that the mechanism of Zongzi is mainly attributed to the rotational resonance attenuation.

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