環境所產生的振動是非常常見的，在講求精密製造中，隔震會變成一個重要的課題。聲子晶體是由兩種不同的彈性材料週期排列而成的結構，此人造結構擁有聲子能隙的特殊現象，可以隔絕聲波或是彈性波在聲子晶體上的傳遞，使特定角度與頻率的彈性波皆無法傳遞通過聲子晶體。
本文利用二次曲線樑設計出手性結構，並先分析其蒲松比；說明了當此結構在受力變形時，會具有負值的蒲松比；並且討論同樣以二次曲線樑所組成的幾種結構的蒲松比。在動態分析下，利用有限元素法分析二次曲線手性結構的色散曲線，藉由判斷色散曲線來分析彈性波是否能傳遞過聲子晶體。本文亦利用二次曲線手性結構設計出點缺陷聲子晶體及局部共振型聲子晶體，點缺陷亦可作為聲子晶體共振腔。配合超晶胞法計算含點缺陷聲子晶體的色散曲線，並分析在缺陷能帶中彈性波侷限在共振腔之中的模態。在局部共振型二次曲線手性結構中，分析局部共振型所產生的原因，計算負質量密度，並藉由全波模擬說明負質量密度與完全能隙之間的關係。

We proposed a new design of quadratic chiral structure with ring and without ring by using curve beam. At first, we analyze static mechanical properties, we find it has negative Poisson’s ratio. Quadratic chiral structure with ring has negative Poisson’s ratio near -1. We also analyze dynamic mechanical properties. When we analyze dispersion relation diagram, the quadratic chiral structure is better than square honeycomb because it has appear more full bandgaps. We also design resonant cavity and locally resonant phononic crystals, and calculate the negative mass density.

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