本文旨在探討薄膜-質量型超穎板的波傳行為，局部的薄膜-質量型共振器可以等效為彈簧-質量系統，故利用Rayleigh-Ritz method計算出薄膜-質量型局部共振器的等效勁度。此外，考慮薄板經過開孔處理後，其材料的機械性質會改變，故分別探討不同孔徑圓孔薄板的等效彈性常數。另一方面，本文利用平面波展開法(Plane Wave Expansion)，提出適用於單頻或多頻局部共振系統的頻散關係計算式，結合擴展平面波法以獲得複數帶隙結構，並進一步減化計算過程，其中虛部帶隙可以顯示系統的衰減狀況。本文使用有限元素模擬軟體驗證理論計算的正確性，比對結果顯示孔洞比例越大，彈性常數的修正效果越佳，且雙共振器未修正時的誤差比單共振器大。同時，在雙頻共振系統中，當兩共振頻率相近時，會有帶隙縮減的現象。針對雙頻共振系統比較單層與雙層共振器，結果顯示雙層共振器可以有效拓寬減振範圍，又以相對高頻的帶隙拓寬效果較明顯。最後透過多頻共振器的設計，以達到多頻減振的效果。

In this thesis, we analyze the propagation of flexural waves in a metaplate with membrane-mass resonators. Based on the Rayleigh-Ritz method, the effective stiffness of the resonator can be calculated. The well-known plane wave expansion (PWE) method is used for the calculation of dispersion relation. Furthermore, we also utilize extended plane wave expansion (EPWE) method to obtain a complex wave band structure. In addition, finite element software (COMSOL Multiphysics) is adopted to verify the theoretical results. On the other hand, the effective elastic constants of the plates with different pitches are discussed. With bigger the perforation size, the accuracy of the modified model is improved. The effect of mass magnitude, membrane tension and the height of the membrane on the frequency of bandgap is investigated. Besides, it is found that the double-layer resonator can broaden the vibration reduction range. Finally, through the design of a multi-frequency resonator, the multi-bandgap can be achieved.

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