地震超材料設計之減震分析及效益評估

AN ASSESSMENT OF ENERGY DISSIPATION EFFECT OF SEISMIC METAMATERIALS

10.6652/JoCICHE.202011_32(7).0003

李冠慧(Guan-Hui Li)；汪向榮(Shiang-Jung Wang)；蘇于琪(Yu-Chi Su)；游忠翰(Chung-Han Yu)；張國鎮(Kuo-Chun Chang)；陳東陽(Tung-Yang Chen)

地震超材料 ； 等效介質理論 ； 減震效益 ； seismic metamaterials ； effective medium theory ； energy dissipation effect

中國土木水利工程學刊

32卷7期（2020 / 11 / 01）

597 - 607

繁體中文

近幾年抗震領域興起了一新穎的減震技術－地震超材料，其透過激發震波頻率下材料的局部共振達到消能目的，因此包圍在保護區域外的超材料單元結構，能迫使地震能量於傳播路徑中受到衰減。本研究為求更貼近實際量化地震超材料的減震效能，首先選定減震效益評估指標與目標地震，然後由等效介質理論出發，說明等效負質量密度與等效彈性模數所對應的共振消能方式，並進一步將其應用於單元結構設計。藉由前述方法，本研究提出對應相對高頻與低頻地震的單元結構，基於波傳去耦合理論基礎下，透過彈性波司乃耳定律驗證了超材料等效介質所具有的震波削減效果。最後，為考量材料真實性並探究超材料層數與減震效能之關聯性，以有限元素分析軟體建立實尺超材料模型，以評估地震超材料在帶隙頻率的減震效益。

Metamaterial is a new type of composite materials, made of artificially structured constituents, that can control different waves in ways not seen in nature. Seismic waves, in contrast to other physical phenomena, correspond to long wavelength and low frequency range. This artificially engineered materials utilize coupling interference mechanism between the propagating waves and internal structure of metamaterial to attenuate or to reroute wave energy at frequencies near local resonances. Previous research along this category focused mostly on the design of material constituents and geometric arrangements of the metamaterials so that local resonances can be achieved within the frequency range. In this work, we aim at providing a quantitative and realistic estimation for energy reduction of ground motion for metamaterial design. We first demonstrate that, within the band gap of the unit cell, the effective homogeneous medium, corresponding either to the negative stiffness or to the negative mass density based on homogenization theory, will convert seismic waves into an evanescent wave. This will result in energy dissipation effect. Further, based on Snell's law, we show analytically that the amplitude and the acceleration can be greatly diminished when harmonic waves are impinged normally on an interface between the soil and an effective homogeneous metamaterial. To simulate practical situations, a real time-acceleration data of the 1999 Chi-Chi earthquake was utilized as external force excitation. Two different sites data (TCU 079 and TCU 045) were selected, which in turn will represent relatively high and low frequency. A full-scale finite element simulation was performed to demonstrate the effectiveness of seismic mitigation, and to examine the width of the waveguide on the energy reduction.

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