基于快速多极间接边界元法的地震超材料隔震效应  

Seismic Isolation Effect of Seismic Metamaterials Based on Fast Multipolar Indirect Boundary Element Method

作　　者：刘中宪 张铭楷[1] 黄磊 黄振恩 LIU Zhongxian;ZHANG Mingkai;HUANG Lei;HUANG Zhenen(School of Civil Eng.,Tianjin Chengjian Univ.,Tianjin 300384,China;Tianjin Key Lab.of Soft Soil Characteristics and Eng.Environment,Tianjin 300384,China;Dept.of Civil Eng.,Tianjin Univ.,Tianjin 300072,China)

机构地区：[1]天津城建大学土木工程学院,天津300384 [2]天津市软土特性与工程环境重点实验室,天津300384 [3]天津大学建筑工程学院,天津300072

出　　处：《工程科学与技术》2024年第2期151-161,共11页Advanced Engineering Sciences

基　　金：国家自然科学基金项目(U2139208,52108466);中国地震局地震工程与工程振动重点实验室重点专项(2020EEEVL0302)。

摘　　要：中国是世界上遭受地震灾害较严重的国家之一。近年来,灾害性地震给人们的生命财产带来了极大的损失,对重大工程结构开展减震隔震设计成为结构设计中重要的一环。本文将快速多极间接边界元法(FMIBEM)应用到2维地震超材料对地震波的散射模拟,并求解一种周期性隔震材料——岩土复合地震超材料(RSCSM)的隔震效应;在精度验证基础上,对RSCSM的带隙结构及不同单晶胞结构下的隔震效果与带隙范围进行详细的数值分析。结果表明:采用FMIBEM能够有效地处理大型地震超材料对地震波的宽频散射问题;RSCSM能够隔离地震波超低频段隙,方形晶胞结构产生的带隙宽度(0.5~17.0 Hz与54.0~72.0 Hz)涵盖了地震波产生危害的主要频段(0.5~2.0 Hz),隔震效果可达35%以上;改变RSCSM的单晶胞结构会对地震超材料带隙结构产生重要影响。方形晶胞结构产生的带隙约为0.5~17.0 Hz和54.0~72.0 Hz;菱形晶胞结构产生的带隙约为0.5~20.0 Hz;菱形单点晶胞结构产生的带隙约为0.5~16.0 Hz和40.0~57.0 Hz;菱形双点晶胞结构产生的带隙约为0.5~14.0 Hz。硬散射体填充率也会对带隙产生重要影响,相同填充率情况下,四边形晶胞能够产生更宽的带隙,并且能够在更低的填充率情况下产生更好的带隙效果。菱形单点与菱形双点晶胞结构只能在非常高的填充率情况下产生较好的带隙效果。本文研究为地震超材料对地震波散射的模拟提供一种高效方法,研究结论可为地基隔震设计提供科学依据。China is one of the countries in the world that have suffered more severely from earthquake disasters.In recent years,catastrophic earthquakes have greatly harmed people's lives and properties.The seismic isolation design of major engineering structures to carry out seismic isolation design has become an indispensable part of the structural design.The Fast Multipole Indirect Boundary Element Method(FMIBEM)was applied to the simulation of seismic wave scattering by 2D seismic metamaterials,and the seismic Isolation effect of a kind of periodic seismic isolation material,i.e.,the geotechnical composite seismic metamaterial(RSCSM),was solved.Based on the accuracy verification,the bandgap structure of RSCSM and the seismic isolation effect and bandgap range under different single-cell structures were numerically analyzed in detail.The results show that the broadband scattering of seismic waves by large seismic metamaterials can be effectively dealt with by using FMIBEM;RSCSM can isolate the ultra-low-frequency bandgap of seismic waves,and the width of the bandgap generated by the square-cell structure(0.5~17.0 Hz and 54.0~72.0 Hz)covers the main frequency bands of seismic wave hazards(0.5~2.0 Hz),with an isolation effect of up to 35%or more;and the effect of changing the single-cell structure of RSCSM can be analyzed.Single-cell structure of RSCSM has an important effect on the seismic metamaterial bandgap structure.The bandgap generated by the square cell structure is approximately 0.5~17.0 Hz and 54.0~72.0 Hz;the bandgap generated by the rhombic cell structure is approximately 0.5~20.0 Hz;the bandgap generated by the rhombic single-dot cell structure is approximately 0.5~16.0 Hz and 40.0~57.0 Hz;and the bandgap generated by the rhombic double-dot cell structure is approximately 0.5~14.0 Hz.The filling rate of the hard scatterer also has an important impact on the bandgap,which can be significantly influenced by the same filling rate.The tetragonal cell produces a wider bandgap at the same filling rate,and the tetra

关 键 词：隔震 超材料 边界元法(BEM) 带隙 

分 类 号：O347.4[理学—固体力学]