在自然界中，質量密度和楊氏模數為描述材料的基本物理性質，其值都是大於零，但人造結構所形成的物質可以實現小於零的材料參數，而這些特殊的物理性質可以有許多可能的應用，如雙負聲學超常材料可以達成負折射現象或次波長成像，而單負聲學超常材料可以應用在聲波或彈性波濾波器。
近年來學者專注於研究聲學超常材料的負質量以及負楊氏模數，而本文主要在研究含次結構的彈簧質量塊週期系統，探討其等效系統，並探討其能量傳遞與波衰減機制，發現在當波傳頻率大於次結構的共振頻率，將其等效質量或等效彈簧常數值為負，且波無法在週期系統中進行傳遞，嘗試結合等效負質量及等效負彈簧常數的彈簧質量塊週期系統，期望可以達到雙負聲學超常材料，但卻發現在等效負質量及等效負彈簧常數的頻率重合區，並沒有觀察到波傳遞的行為。
此外，本研究提出一含次結構的彈簧質量塊週期系統設計，主要在用於增加能隙，可作為寬能隙的濾波器，本文探討兩種不同設計，第一種是學者所提出的採用多重次結構週期系統，結合不同次結構的共振來達到能隙範圍的增加，第二種為本研究所提出採用雙原子系統的概念加入次結構，彈簧質量塊組合與多重次結構完全相同，經比較兩種週期系統設計皆對波的吸收有效果，但第二種設計有明顯較寬的能隙。

The mass density and the Young's modulus are used to describe the basic physical properties of the material. These natural material properties are positive. However, negative material can be achieved by artificially-structured material, and these negative properties of acoustic metamaterial will offer many opportunities in the wave engineering. For example, double negative acoustic metamaterial would demonstrate negative refraction behavior or subwavelength image. Single negative metamaterial could be employed as acoustic and elastic wave filters.
Recently, many researchers focused on the study of negative mass and negative Young’s modulus of acoustic metamaterials. Our research investigated the wave propagation behavior inside mass-spring periodic system including sub-structures. We studied the wave attenuation mechanism and how the energy distributed between sub-structure and major structure. It was found that the wave could not propagate inside the periodic system if the wave frequency was higher than the resonance of the sub-structure. And the equivalent mass or spring constant was negative. We attempted to combine the periodic systems with negative mass and negative spring constant so that the double negative system could be achieved. However, the wave still could not propagate within the overlapped frequency range in finite element simulation. Further investigation is needed in order to explain the underlying mechanism.
Besides, we proposed a periodic spring-mass system design in order to enlarge the bandgap so that wide bandgap filter could be realized. In this research, two designs of periodic systems were studied. One design was proposed in the literature by including several sub-structures into the system. The bandgap would be enlarged by combining the resonance of the sub-structures. Our proposed design was adopting the diatomic chain concept with sub-structures so that the resonance of the sub-structure would fall within the bandgap of acoustic and optical branches. It was observed that both designs could effectively attenuate wave. However, our proposed design clearly demonstrated a wider bandgap under the same mass and spring constitutions.

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