本論文旨在探討超材料的幾何可調性，特別是從圓形內含物擴展至橢圓形內含物。參考林宗穎(2023)的研究，進一步探討橢圓形內含物在不同長短軸比值下的頻散曲線變化及局部共振消能機制。發現橢圓超材料因長短軸的差異，發展出圓形超材料所不具有的方向性及可調性。然而，林宗穎(2023)提出的橢圓超材料模型在改變幾何形狀時採取固定長軸長度同時縮短短軸的方式，會導致材料體積比產生變化，進而導致體積比亦成為影響局部共振頻率及帶寬的因素之一。因此，本論文改良林宗穎(2023)提出的橢圓超材料模型，使單元結構在改變幾何形狀時始終保持相同材料體積比，以利更專注於探討幾何形狀對超材料消能機制的直接影響。首先利用平面波展開法生成頻散圖，驗證體積比對頻帶的影響，並使用有限元素軟體COMSOL計算橢圓超材料的各種等效係數，分析不同共振模態下的消能機制及帶隙隨長短軸比值的變化。接著，通過半全域模擬進一步探討橢圓超材料對縱波及剪切波的衰減效果，嘗試找出最佳消能組合。
本論文展示了橢圓超材料在幾何可調性和方向性上的優勢，通過詳細的模擬和分析，證明其在局部共振頻率及帶寬調控上的潛力，為未來超材料的設計和應用提供了新的思路和方法。

In this thesis, we investigate the geometric tunability of metamaterials, extending the study from circular inclusions to elliptical inclusions. Our findings indicate that elliptical metamaterials exhibit superior tunability compared to circular metamaterials due to the differences in the major and minor axes. We build upon the elliptical metamaterial model proposed by Lin(2023), ensuring that the unit cells maintain a consistent material volume fraction when altering geometric shapes. This approach allows us to focus more precisely on the direct impact of geometric shape on the energy dissipation mechanisms of metamaterials. Firstly, we employ the plane wave expansion method to generate dispersion diagrams, verifying the impact of volume fraction on the bandgaps. Secondly, we use finite element method to calculate various effective modulus of elliptical metamaterials, analyzing the energy dissipation mechanisms and the variations in bandgaps under different resonant modes as the aspect ratio changes. Subsequently, we use numerical simulations to explore the attenuation effects of elliptical metamaterials on longitudinal and shear waves, attempting to identify the optimal energy dissipation combination. Lastly, beyond demonstrating the advantages of elliptical metamaterials in terms of geometric tunability and directionality, we also prove their potential in controlling local resonance frequency and bandwidth. These provide new insights and methods for the future design and application of metamaterials.

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