Clamped seismic metamaterials: ultra-low frequency stop bands
Clamped seismic metamaterials: ultra-low frequency stop bands
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DOI：
10.1088/1367-2630/aa6e21
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发表时间：
2017-06-16
影响因子：
3.3
通讯作者：
Guenneau, S.
中科院分区：
文献类型：
--
作者：
Achaoui, Y.;Antonakakis, T.;Guenneau, S.
地震的规律性，其破坏力，以及城市环境中地面振动的滋扰，都促使防御结构的设计，以减少地震和地面振动波对建筑物的影响。低频波，如地震在1-10赫兹范围内，而人类活动产生的振动则高达几十赫兹，会造成大量的破坏或不便；根据地质条件的不同，它们可以传播相当远的距离，并且可能与建筑物的共振基频相匹配。任何地震超材料或任何其他地震屏蔽物的最终目的，都是在整个频率范围内进行保护；涉及到的波长长，频率低，这意味着到目前为止还无法实现。值得注意的是，这是可扩展的，效果也适用于较小的超声波设备。获得屏蔽效果的方法有三种：布拉格散射、局部谐振亚波长内含物和零频率阻带介质。前两者已经探讨过了，但后者还没有，在这里进行考察。弹性弯曲波，适用于薄弹性板的机械振动，可以设计成有一个宽的零频率阻带，使用一个非常小的夹紧圆的周期阵列。受实验和理论观察的启发，所有这些都是在远离地震波的情况下进行的，我们证明了在结构化土壤中实现弹性表面（瑞利）波反射器在非常大的波长下是可能的，这些土壤被建模为周期性夹在基岩上的完全弹性层。我们确定了零频率止动带，这些止动带只存在于混凝土柱的极限中，这些混凝土柱的底部被固定在基岩上。在一个15m深的沉积盆地的实际构造中，我们观察到一个覆盖0-30 Hz宽频率范围的零频率阻带。
The regularity of earthquakes, their destructive power, and the nuisance of ground vibration in urban environments, all motivate designs of defence structures to lessen the impact of seismic and ground vibration waves on buildings. Low frequency waves, in the range 1-10 Hz for earthquakes and up to a few tens of Hz for vibrations generated by human activities, cause a large amount of damage, or inconvenience; depending on the geological conditions they can travel considerable distances and may match the resonant fundamental frequency of buildings. The ultimate aim of any seismic metamaterial, or any other seismic shield, is to protect over this entire range of frequencies; the long wavelengths involved, and low frequency, have meant this has been unachievable to date. Notably this is scalable and the effects also hold for smaller devices in ultrasonics. There are three approaches to obtaining shielding effects: bragg scattering, locally resonant sub-wavelength inclusions and zero-frequency stop-band media. The former two have been explored, but the latter has not and is examined here. Elastic flexural waves, applicable in the mechanical vibrations of thin elastic plates, can be designed to have a broad zero-frequency stop-band using a periodic array of very small clamped circles. Inspired by this experimental and theoretical observation, all be it in a situation far removed from seismic waves, we demonstrate that it is possible to achieve elastic surface (Rayleigh) wave reflectors at very large wavelengths in structured soils modelled as a fully elastic layer periodically clamped to bedrock. Weidentify zero frequency stop-bands that only exist in the limit of columns of concrete clamped at their base to the bedrock. In a realistic configuration of a sedimentary basin 15m deep we observe a zero frequency stop-band covering a broad frequency range of 0-30 Hz.