聲子晶體為兩種或兩種以上的材料經週期性排列組合而成，若將其週期性破壞會使結構型成缺陷，一般聲子晶體共振腔即利用點缺陷形成。本文利用一保角映射函數將原本正方晶格或三角晶格之完美聲子晶體轉換成另一結構，由於函數的特性，可在新結構中心產生一個空腔，當聲波入射此結構時會在空腔內產生Fabry-Pero共振，在共振腔中形成共振模態，與一般聲子晶體共振腔比較後，發現轉換後之聲子晶體共振腔之壓力放大特性與品質因子皆較為理想。再將原始聲子晶體之填充率逐漸加大，經轉換過後發現當填充率越大聲壓放大效應與品質因子皆有更為良好之效果。再進一步而探討原始聲子晶體之分布位置，經轉換後可以利用本文所提出之方法將共振頻率無因次化，使得結構可依吾人所需求之共振頻率來設計；對三角晶格聲子晶體的晶格點進行調整，使正三角形變型，再經過保角映射後，發現由於結構之對稱性慢慢被破壞，使得共振模態逐漸消失。最後以實驗印證正方晶格聲子晶體與其轉換之結構計算結果。

Phononic crystals are artificial structures with periodically varying material parameters. Generally, a phononic cavity is formed by creating a point defect in a perfect phononic crystal. In this study, a novel sonic cavity structure is formed by conformal mapping function transformation of square and triangular lattice sonic crystals. The new cavity structure will be at the center of the sonic crystal. Fabry-Pero resonances can be observed in the cavity when sonic waves propagate through the sonic crystal. Compared with original sonic crystal with a point defect (a original structure remove a rod to form a sonic cavity), the pressure amplication and the quality factor of the new sonic crystal is better than those of original one. The higher acoustic pressure is formed in the cavity and the quality factor of the cavity increases as the filling fraction of the original crystal (perfect crystal) increases. Furthermore, the normalize resonance frequencies of transformed crystals can be evaluated according to the mapping function. We obtain the size of sonic crystal in terms of the desired resonance frequency. The conformal transformation of distorted triangular lattice crystals are also presented. It is observed that the resonance modes will disappear because symmetry of such structures is destroyed. Finally, the simulation results of square lattice sonic cavities and the transformation structure were confirmed by experiments.

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