超材料的特殊機制與其發展性在近年來被廣為討論與研究，相對於電磁超材料與聲學超材料，學者們發現了彈性超材料(elastic metamaterials)在濾波方面能更有發展性。為了使彈性超材料發揮更佳的過濾向量波傳遞特性，因此本文會先介紹波傳的基本理論與其等效參數與波傳特性間的探討，最後再根據上述的理論關係式並透過有限元素分析軟體COMSOL數值分析模擬，建立立方晶格(cubic lattice)與六方晶格(hexagonal lattice)的連體模型作探討，並以其運動模式與等效參數和全域模擬加以驗證。由於噪音與機械共振多屬於低頻波且有衰減較慢的特性，常造成較大影響，因此本文透過晶格尺寸與自然界容易取得的材料加以篩選，提出的模型較著重於能夠產生較低且較寬的帶隙(band gap)頻率範圍，以達到更佳的濾波效果，並透過兩種晶格的比較結果發現六方晶格有較立方晶格還寬的帶隙。

The mechanism of metamaterials and their development are widely discussed and studied in recent years. Compared with electromagnetic metamaterials and acoustics metamaterials, researchers found that elastic metamaterials can be developed in terms of filtering. In order to have a better filtering property in elastic metamaterials, we will first introduce the basic theory of wave propagation and the concept of effective medium. Two models are proposed, cubic lattice and hexagonal lattice, with finite element analysis to simulate compare the results. Finally, the eigenstates, the effective mass density and wave transmission simulation are used to verify. Noise and mechanical resonance are mostly low frequency waves. The lower frequency of the wave often causes a great impact because of slow attenuation characteristics. In this thesis, we change the lattice size and materials in order to attain a wide band gap elastic metamaterials that can filter out low frequency waves. Based on the results of two lattices, we found that the hexagonal lattice has a wider band gap than that of the cubic lattice.

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