近年來，局部共振的聲學超穎材料在低頻時有著良好的隔音效果。低頻噪音是在動力機械運轉上常會遇到的問題，這種噪音很難被傳統的混凝土擋土牆所隔絕，但是如果使用聲學超穎材料，就能很容易達成這個目標。雖然這些超穎材料很輕，但依然可以用於隔音。在此篇論文中，我們使用理論模型與分析圓形薄膜質量系統的穿透損失，之後使用有限元素軟體去計算聲學超穎材料用來探討其隔音效果。此篇論文我們討論薄膜與質量在調整質量重量、面積、以及作用於薄膜上的預拉力對於穿透損失、有效質量、聲功率的影響，更進一步考慮在多個質量體下的曲線變化。再者，調整質量體的搭配，由一個中心質量體改變為環形質量與多個質量體，可以看出在各曲線上會產生多個波峰與波谷的情況，而且我們可以調整質量放置位置、表面密度、質量數量都能看到在改變薄膜與質量的性質所帶來的影響，進而產生多個有效頻率。

In recent years, locally resonance acoustic metamaterials have displayed feasible sound insulation capabilities at low frequencies. Low frequency noise is often generated by machines when they are being operated and is difficult to be blocked by a traditional heavy concrete wall. Using acoustic metamaterials, sound insulation is much easier to be achieved. Although these metamaterials is usually light and thin, they still work well for insulating noise. In this thesis, we present a theoretical method to investigate transmission loss of circular membranes with mass inclusions, and the analytical results are compared with finite element results. We then discuss the characteristics of transmission loss (TL), effective dynamic mass, and sound power flow. We adjusted the mass weight, area and the pretension force on the edges of the membrane and considered their effect on TL curves. Furthermore, the central mass embedded in the structure was replaced by the ring mass, and we also considered a membrane with both one central mass and one ring mass or a membrane containing two masses. The TL valley and peak frequency and bandwidth can be tuned by varying surface density, the number of rings, and ring locations.

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