西安建筑科技大学学报(自然科学版)

针对破坏力极强的地震表面波中瑞利波的振动控制,提出一种新型半埋入式地震超材料屏障.相比于传统的地震超材料屏障,这种新型半埋入式超材料屏障将单胞的内外柱体分别单独半埋入土壤中,结构稳定性强且具有低频宽带隙特性.采用有限元法计算了新型半埋入方式下地震超材料屏障的带隙特性,并结合其振型分析了带隙的形成机理,当内外柱体分别单独半埋入时,振子和振动模态各不相同,打开了不同的低频带隙.进一步分析了埋入深度、连接体杨氏模量的变化对带隙机理的影响,其中,埋入深度是影响带隙的主要因素,随着埋入深度的增加,屏障稳定性增强,系统的主导刚度会发生改变,引起了局域共振模态的转变,从而拓宽带隙的宽度.最后,对有限周期模型屏障的振动传输特性进行了计算,并通过EI-Centro地震波对屏障进行了时程分析,加速度幅值衰减超过70%.结果表明:新型半埋入式地震超材料屏障对20 Hz以下的瑞利波具有良好的衰减作用,为地震超材料在减震隔震方面提供新的设计思路和方法.

A new type of semi-buried seismic metamaterial barrier is proposed for vibration control of Rayleigh waves in seismic surface waves with strong destructive force. Compared with the traditional seismic metamaterial barrier, this new semi-embedded metamaterial barrier semi-embedded the inner and outer columns of the unit cell into the soil separately, which has strong structural stability and low-frequency broadband gap characteristics. The finite element method is used to calculate the band gap characteristics of the seismic metamaterial barrier under the new semi-buried mode, and the formation mechanism of the band gap is analyzed combined with its vibration mode. When the internal and external columns are semi-buried separately, the oscillator and the vibration mode are different, and the low frequency band gap is opened. The influence of the embedded depth and Young's modulus of the connector on the band gap mechanism is further analyzed. The embedded depth is the main factor affecting the band gap. With the increase of the embedded depth, the stability of the barrier is enhanced, and the dominant stiffness of the system will change, resulting in the change of the local resonance mode, thus broadening the width of the band gap. Finally, the vibration transmission characteristics of the finite periodic model barrier are calculated, and the time history analysis of the barrier is carried out by EI-Centro seismic wave. The acceleration amplitude attenuation is more than 70%. The results show that the new semi-buried seismic metamaterial barrier has a good attenuation effect on Rayleigh wave below 20 Hz, which provides a new design idea and method for seismic metamaterials in damping and isolation.

引言
1 模型和计算方法
2 数值结果和分析
3 频域和地震动时程分析
4 结论

图1 新型半埋入式屏障结构<br/>Fig.1 New semi-embedded barrier structure

图1 新型半埋入式屏障结构
Fig.1 New semi-embedded barrier structure

表1 屏障结构材料参数<br/>Tab.1 Barrier structure material parameters

表1 屏障结构材料参数
Tab.1 Barrier structure material parameters

图2 不可约Brillouin区<br/>Fig.2 Reduced Brillouin zones

图2 不可约Brillouin区
Fig.2 Reduced Brillouin zones

图3 模型1和模型2能带结构<br/>Fig.3 Band structure of model 1 and model 2

图3 模型1和模型2能带结构
Fig.3 Band structure of model 1 and model 2

图4 能带特殊点的模态振型图<br/>Fig.4 Mode shape diagram with special points

图4 能带特殊点的模态振型图
Fig.4 Mode shape diagram with special points

图5 模型1连接体杨氏模量对带隙的影响<br/>Fig.5 Band gap varied with the changes of Young's modulus of model 1 connector

图5 模型1连接体杨氏模量对带隙的影响
Fig.5 Band gap varied with the changes of Young's modulus of model 1 connector

图6 外部柱体埋入深度h0对带隙的影响<br/>Fig.6 Band gap varied with the changes of the embedding depth h0 of the external cylinder

图6 外部柱体埋入深度h0对带隙的影响
Fig.6 Band gap varied with the changes of the embedding depth h0 of the external cylinder

图7 h0=0.1 m和h0=1.6 m时能带结构和特殊点模态图<br/>Fig.7 Band structure and special point modal diagram of h0=0.1 m and h0=1.6 m

图7 h0=0.1 m和h0=1.6 m时能带结构和特殊点模态图
Fig.7 Band structure and special point modal diagram of h0=0.1 m and h0=1.6 m

图8 模型2连接体的杨氏模量对带隙的影响<br/>Fig.8 Band gap varied with the changes of Young's modulus of model 2 connector

图8 模型2连接体的杨氏模量对带隙的影响
Fig.8 Band gap varied with the changes of Young's modulus of model 2 connector

图9 内部柱体埋入深度h0对带隙的影响<br/>Fig.9 Band gap varied with the changes of the embedding depth h0 of the inner cylinder

图9 内部柱体埋入深度h0对带隙的影响
Fig.9 Band gap varied with the changes of the embedding depth h0 of the inner cylinder

图10 h0=1 m时能带结构和特殊点模态图<br/>Fig.10 Band structure and special point modal diagram of h0=1 m

图10 h0=1 m时能带结构和特殊点模态图
Fig.10 Band structure and special point modal diagram of h0=1 m

图11 频率响应和时域分析计算模型<br/>Fig.11 Frequency response and time domain analysis calculation model

图11 频率响应和时域分析计算模型
Fig.11 Frequency response and time domain analysis calculation model

图12 方向带隙及传输特性曲线<br/>Fig.12 Directional bandgap and transmission characteristic curve

图12 方向带隙及传输特性曲线
Fig.12 Directional bandgap and transmission characteristic curve

图13 带隙内外频率点位移场分布<br/>Fig.13 Frequency displacement field distribution inside and outside the band gap

图13 带隙内外频率点位移场分布
Fig.13 Frequency displacement field distribution inside and outside the band gap

图14 EI Centro地震波<br/>Fig.14 EI Centro seismic wave

图14 EI Centro地震波
Fig.14 EI Centro seismic wave

图15 EI Centro地震波加速度响应<br/>Fig.15 EI Centro seismic wave acceleration response

图15 EI Centro地震波加速度响应
Fig.15 EI Centro seismic wave acceleration response

[1] 崔杰,张为,张建国.Rayleigh波对浅地表地基震害的影响[J].华南地震,2008(2):10-18.
[2]薛建阳,张崇新,韦亮陆,等.附设黏滞阻尼器超高层结构的减震效果分析[J].西安建筑科技大学学报(自然科学版), 2020,52(1):21-29.
[3]钱登辉, 史治宇. 局域共振型周期双层板简化模型带隙特性研究[J]. 振动、测试与诊断, 2019, 39(4):884-891.
[4]WANG G, WEN J, LIN Y, et al. Lumped-mass method for the study of band structure in two-dimensional phononic crystals[J]. Physical Review B, 2004, 69(18):184302.
[5]SHI Z, MENQ, YAN, et al. Three dimensional periodic foundations for base seismic isolation[J]. Smart Materials & Structures, 2015:075006.
[6]DU Qiujiao, ZENG Yi, HUANG Guoliang, et al. Elastic metamaterial - based seismic shield for both Lamb and surface waves[J]. AIP Advances, 2017, 7(7):075015.
[7]PU X, SHI Z. Broadband surface wave attenuation in periodic trench barriers[J]. Journal of Sound and Vibration,2020,468.
[8]MESEGUER F, CABALLERO D, HOLGADO M,et al. Rayleigh-wave attenuation by a semi-infinite two-dimensional elastic-band-gap crystal[J]. Physical Review B, 1999, 59(19):12169-12172.
[9]BRULE S, JAVELAUD E H, ENOCH S, et al. Experiments on seismic metamaterials: molding surface waves[J]. Physical Review Letters, 2014, 112(13):1-5.
[10]PALERMO A, KRDEL S, MARZANI A, et al. Engineered metabarrier as shield from seismic surface waves[J]. Rep, 2016, 6:39356.
[11]MINIACI M, MINIACI M, KRUSHYNSKA A, et al. Large scale mechanical metamaterials as seismic shields[J]. New Journal of Physics, 2016, 18(8):083041.
[12]ACHAOUI Y, ANTONAKAKIS T, BRULE, S, et al. Clamped seismic metamaterials: Ultra-low broad frequency stop-bands[J]. New Journal of Physics, 2017, 19(6):063022.
[13]MANADAL P, SOMALA S N. Periodic pile-soil system as a barrier for seismic surface waves[J]. SN Applied Ences, 2020, 2(7):1184.
[14]DU Qiujiao, ZENG Yi, YANG X, et al. H-fractal seismic metamaterial with broadband low-frequency bandgaps[J]. Journal of Physics, D. Applied Physics: A Europhysics Journal, 2018, 51(10):105104.
[15]MUHAMMD, LIM C W, REDDY J N. Built-up structural steel sections as seismic metamaterials for surface wave attenuation with low frequency wide bandgap in layered soil medium[J]. Engineering Structures, 2019, 188(JUN.1): 440-451.
[16]LIU Ze, QIN Kaiqiang, YU Guilan. Partially embedded gradient metabarrier: Broadband shielding from seismic rayleigh waves at ultralow frequencies[J]. Journal of Engineering Mechanics, 2020, 146(5):04020032.
[17]秦凯强, 刘泽, 于桂兰. 具有低频超宽衰减域的部分埋入式表面波屏障[J]. 地震工程与工程振动, 2020, 40(2):189-196.
[18]刘岩钊. T形部分埋入周期/梯度表面波屏障隔震性能研究[D]. 北京:北京交通大学,2019.
[19]OUDICH M, ASSOUAR M B. Surface acoustic wave band gaps in a diamond-based two-dimensional locally resonant phononic crystal for high frequency applications[J]. Journal of Applied Physics, 2012, 111(1):2022-R.
[20]温熙森,温激鸿,郁殿龙,等.声子晶体[M].北京:国防工业出版社,2009.
[21]KHELIF A, ACHAOUI Y, BENCHABANE S, et al. Locally resonant surface acoustic wave band gaps in a two-dimensional phononic crystal of pillars on a surface[J]. Physical Review B Condensed Matter, 2010, 81(21):1601-1614.
[22]HUANG J, SHI Z, HUANG W. Multiple band gaps of phononic crystals with quasi-Sierpinski carpet unit cells[J]. Physica B Condensed Matter, 2017, 516:48-54.
[23]COLQUITT D J, COLOMBI A, CRASTER R V, et al. Seismic metasurfaces: Sub-wavelength resonators and Rayleigh wave interaction[J]. Journal of the Mechanics & Physics of Solids, 2016, 99:379-393.
[24]Peer Ground Motion Database [EB]. http://peer. berkeley. edu/peer_ground_motion_database, 2018-03-10.

备注

引言

1 模型和计算方法

2 数值结果和分析

3 频域和地震动时程分析

4 结论

期刊信息