地震超材料設計之減震分析及效益評估

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.