超穎材料為一種具有天然材料所不具備之超常物理性質之人工結構或複合材料，其超常物理性質可能包括負質量、負折射率、負體積模數等，且其性質往往不決定於構成材料本身，而決定於其中的人工構造。超穎材料之概念一開始被應用在電磁波領域，近年來逐漸拓展到聲學及彈性波領域。透過特殊設計之負質量超穎材料結構單元使的波傳在特定頻段之衰減達到減振之目的。
本文建立一具有負質量效應之結構單元，其可以分為中央鏤空主樑與嵌在該主樑內部之子結構，該子結構為一附有中央質量塊之雙螺旋結構樑。透過有限元素軟體COMSOL模擬該結構單元之波傳現象，驗證其負質量效應之發生，並觀察頻散曲線中之結構模態得知其能隙與負質量效應之產生原因為子結構之共振現象。本文提出兩種理論模型計算子結構之自然共振頻率，計算結果皆與模擬大致相吻合，且自然共振頻率均落在負質量效應與能隙之起始位置附近。
增加子結構之質量塊可以有效降低子結構共振頻率，因此，本研究透過調整質量塊厚度或是子結構樑的厚度、寬度來控制結構之共振頻率，並觀察相對應結構單元之頻散曲線與負質量效應之變化，結果顯示改變質量塊厚度後之子結構共振頻率亦可以大致吻合負質量效應與能隙之起始位置，從而達到調控結構之減振區頻段的目的。

This thesis presents a novel metamaterial beam with periodic substructures. Each cell consisted of two parts: a host beam with central hole and a substructure embedded in it. The substructure is comprised of a double-spiral beam with a central mass. With the finite element software COMSOL Multiphysics, the dynamic behavior of the metamaterial beam is investigated. The simulated results demonstrated that the band gap and negative mass exist in such a structure. Moreover, two theoretical models were proposed to calculate the natural frequency of the substructure. Both calculations approximately matched with simulation results. The error is less than 5%. The natural frequency of the substructure was close to the starting frequency of the band gap. By adjusting dimensions of the substructure, control of the vibration attenuation zone in the structure can be achieved.

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