地震超材料透過控制波傳的技術達成減震的效果，在近年逐漸吸引眾
多學者投入相關研究。以橡膠包裹內含物為常見的地震超材料的型態，利
用局部共振之機制，達成令入射波消能的效果，降低地震對人類社會的危
害。考量橡膠為黏彈性材料受單向作用力具潛變與鬆弛的特性，並於週期
性運動中具阻尼效應對能量之消散產生貢獻，因而對此議題進行深入探討，
了解黏彈性材料對帶隙的影響。首先介紹彈性內質量模型的消能機制與相
關參數對帶隙的控制。而後推導將彈性材料更換為黏彈性材料後的行為，
並引用實際之材料參數進行討論，說明黏彈性材料之阻尼效應可拓寬帶隙
頻寬但影響程度並不顯著。最後以物理軟體進行模擬，以傳遞率之概念驗
證超材料對於振幅衰減的效果，並與理論推導的成果相互對照，驗證於特
定之頻域波的振幅確實受影響而減小，並進行相關之探討。

A few metamaterials have been utilized to protect structures under earthquakes in recent years. Many geophysical scale experiments have been done to verify the effectiveness of seismic metamaterials. Composite cylinder made of steel core coated with rubber material is commonly used in the design of seismic metamaterials. In light of the viscoelastic property of the rubber, in this thesis we proposed a
viscoelastic mass-in-mass system and discuss the wave attenuation mechanisms of this periodic structure. Firstly, we briefly introduce the elastic mass-in-mass system and demonstrate the tendency toward different sets of mass ratios and stiffness ratios.
Next, the dissipation relation of the viscoelastic mass-in-mass system is derived based on equation of motion and Bloch’s theorem by adding node in the discrete model of viscoelastic material. By incorporating the damping effect of viscoelastic material in consideration, the result shows that bandgap could be extended. Finally, we use a physics simulation software to prove the effectiveness of wave attenuation in viscoelastic mass-in-mass systems for specific frequency ranges.

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