本研究提出壓電圓環分流電路共振器之超穎圓形軸結構，探討壓電圓環分流電路對扭轉控制的可行性。傳統的被動式控制皆需透過幾何模型的改變，才能控制局部共振帶隙的位置，造成調控設計上的困難，本研究藉由壓電圓環附加外部電路，期望有效的達到主動式控制局部共振帶隙特徵的目的。基於壓電本構方程式及一維扭轉振動全域方程式，並藉由布洛赫邊界條件，以轉換矩陣法可推導出超穎結構之頻散關係與頻率響應圖。本研究分別討論被動電路、主動式並聯負電容電路及主動式串聯負電容電路三種分流電路。發現使用主動式串聯負電容電路之超穎結構，可維持局部共振帶隙在1000–2000 Hz之間，同時達到寬頻的減振頻段，並發現透過參數改變可調控帶隙位置。本研究同時使用有限元素模擬軟體COMSOL Multiphysics，模擬有限週期單元數之超穎結構在扭傳振動下的波傳行為。根據模擬結果，可以在局部共振帶隙的頻率位置發現減振頻段，並且理論與模擬的結果相當一致。最後，本研究延伸討論雙共振器之超穎結構，透過兩外部電路的調控，達到主動式控制雙局部共振帶隙特徵的效果，更利於在工程方面的應用。

This thesis presents a novel metamaterial shaft composed of a host shaft with periodic arrays of shunted piezoelectric rings. By tuning the circuital parameters, the bandgap characteristics can be effectively adjusted. Based on transfer matrix (TM) method and Bloch’s theory, theoretical models are introduced. Finite element software COMSOL Multiphysics is utilized to simulate the transmission behavior of the metamaterial shaft. The effects of circuital parameters on band gaps are analyzed. The lower frequency location and wider bandwidth of band gaps can be achieved with NCER shunt. Moreover, a metamaterial shaft. with double resonators is further introduced to attain multiple bandgaps.

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