超材料是一種為了滿足特定需求所加工出來的人造材料，透過微結構精心的幾何設計與性能來加以調控，因此可以產出前所未有的特殊機構如負柏松比結構或剪力模數遠小於體積模數的五模超材料，而本論文所探討的是一種全新的機械超材料，一種微結構與傳統小吃粽子形狀極為相似的類粽子型超材料，其微結構之幾何對稱使得材料在巨觀下具有立方對稱的材料對稱性質，而經由有限元素軟體的分析搭配複合材料理論，我們了解到此超材料同五模具有體積模數與剪力模數相比原始材料而言能夠小上幾個量級的極端性質，且此類粽子型超材料具有優越的可調性，藉由微結構簡易的改變將能夠調動超材料之等效材料參數、等效質量密度以及整體材料的異向性行為，而這些機制背後最強大的支撐點為此粽子結構僅由單一簡易的代數方程式即可表述，而本文除了計算類粽子型超材料於靜態下的力學分析之外，也有針對超材料的頻散曲線做討論，經由有限元素軟體的掃頻方式來瞭解此結構於波傳下的反應為何，而從初步的分析中發現到粽子超材料在特定頻率區間具有帶隙的情況產生，且隨著結構與原始材料的不同，帶隙頻率範圍將能夠有所調整，而後期望能夠再進一步藉由全域模擬的方式來加以驗證頻散曲線的正確性與合理性。

Mechanical metamaterials are man-made materials that exhibit properties and functionalities that cannot be realized by conventional materials. They are regulated through careful geometric design and performance of microstructures. In this thesis we discuss a new type of mechanical metamaterial whose microstructure is similar to the shape of a Chinese food, “Zongzi”. The geometric symmetry of the microstructure causes the material to possess cubic elastic symmetry, therefore have two kinds of different shear deformation mode. Through the analysis of finite element software and the theory of composites, we find that the Zongzi-like metamaterial holds extreme properties such as its effective bulk and shear modulus smaller than the constituent material. Furthermore, we demonstrate the tunability of the microstructure, resulting in changing the equivalent elastic parameters, changing the equivalent mass density and the anisotropic behavior of the overall material. Lastly, we calculate the dispersion curve and show that the Zongzi-like metamaterial exhibit band-gaps which wave can be attenuated in certain frequency ranges. In addition, the band-gap range can be adjusted through different parameters.

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