聲子晶體是由兩種或兩種以上不同的彈性材料或流體週期排列而形成的結構，此人造結構會使得某些頻率或是某些特定入射角度之聲波或彈性波被禁止傳遞通過此週期性結構，產生能隙現象。當完美的週期性結構被破壞，若移除單一聲子晶體填充物產聲點缺陷可形成共振腔，或是移除整排聲子晶體填充物產生線缺陷可形成波導，此時將會在能隙範圍內產生缺線模態，在缺陷模態的頻率之下，能夠將聲波或彈性波侷限在聲子晶體之缺陷中，缺陷模態所對應的頻帶即為缺陷頻帶，此種特性可應用於濾波器，或是各種隔音裝置上。三角晶格與正方晶格是聲子晶體常見的晶格排列方式，阿基米德晶格則是由一種以上的正多邊形來排列成整個平面，並且沒有產生任何縫隙，此種晶格可以達到傳統晶格所無法達成的旋轉對稱性。
本文使用平面波展開法以及有限元素法求得聲子晶體之色散曲線，進而結合超晶胞法計算阿基米德晶格之色散曲線以及含缺陷聲子晶體之色散曲線，並且探討在三角晶格與阿基米德晶格下色散曲線之差異，也分析共振模態之壓力場與品質因子。在阿基米德晶格聲子晶體之共振腔中排放不同層數的聲子晶體填充物，觀察其壓力場與共振頻率的變化，並且改變填充物的半徑大小，以了解此變化是否會影響壓力場以及品質因子。

We considered phononic crystals with Archimedean tilings and triangular lattice arrangement, which were consisted of PMMA cylinders in the air background. The number of band gap for phononic crystal with Archimedean tilings is more than that with triangular lattice arrangement within frequency of 0-10000Hz. In the defect of phononic crystals with Archimedean tilings, we observed whispering-gallery-mode of resonance, which can promote the quality factor. We put different radius of scattering inclusions to form a smaller circle in the cavity to tune the resonant frequencies. On the other hand, we put a hollow cylinder scattering inclusion in the cavity makes quality factor be enhanced.

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