Clamped seismic metamaterials: ultra-low frequency stop bands

Abstract

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 zerofrequency 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. We identify 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 15 m deep we observe a zero frequency stop-band covering a broad frequency range of 0-30 Hz. and horizontally polarized Love waves), pressure bulk waves and shear bulk waves; surface waves cause the majority of any damage and travel farthest, but bulk pressure, and shear, waves also cause damage, especially where wave trapping occurs in sedimentary basins (so-called seismic site effects). Designing a defence structure to prevent seismic waves from reaching buildings is therefore of substantial interest particularly for long waves with frequency in the range 1-10Hz as this corresponds to the resonant fundamental frequency of many manmade structures [3]. It is, of course, these long, low frequency, waves that are the hardest to develop protection measures against and it is an open problem to develop such devices.Since the late 1980s, in optics, researchers have taken advantage of technological improvements in structuring matter to achieve control over the flow of light [4,5]. The photonic crystals typically used are periodic man-made structures that inhibit emission due to band gaps [6, 7], i.e., ranges of frequency in which light cannot propagate through the structure. The existence of stop-bands is well predicted by Floquet-Bloch theory, which can be...

Role of nanophotonics in the birth of seismic megastructures

“…The first type includes structured soils made of cylindrical voids ( [2] and [3]) or rigid inclusions ( [5] and [6]), including seismic metamaterials. This group is called "Seismic Soil-Metamaterials" or SSM in short.…”

“…The second group of seismic metamaterials consists of resonators buried in the soil in the spirit of tuned-mass dampers (TMD) like those placed atop of skyscrapers [7][8][9][10]. We call this group "Buried Mass-Resonators" (BMR).…”

“…One way to cancel the elastic signal of such antennae is to implement the concept of external cloaking, see FIG. 8., whereby negatively refracting isotropic elastic layers placed nearby 9 clamped inclusions (such as concrete columns in soil clamped to a bedrock creating a zero frequency stop band in [7]), reduce dramatically the scattering of a plane (flexural) incident wave. The same holds true for stress-free inclusions, such as boreholes in soil, or for buildings placed atop a soil.…”

Elastic Wave Control Beyond Band-Gaps: Shaping the Flow of Waves in Plates and Half-Spaces with Subwavelength Resonant Rods

“…Devices based on exploiting band-gap phenomena, as seismic shields using ideas from Bragg-scattering (Brûlé et al, 2014;Miniaci et al, 2016) or zero-frequency stop-bands (Achaoui et al, 2017), are gaining in popularity. At this large scale, an important analogy may exist between the metamaterial discussed here and clusters of high-rise buildings in urban areas.…”

“…If we limit our discussion to elastic metamaterials, potential applications could be implemented at any lengthscale. On the large scale, seismic metamaterials have become very popular (Brûlé et al, 2014;Finocchio et al, 2014;Dertimanis et al, 2016;Miniaci et al, 2016;Achaoui et al, 2017). At smaller scale, in mechanical engineering, applications based on wave redirection and protection are currently being explored (Colombi, 2016;Colombi et al, 2017) to reduce vibrations in high precision manufacturing and in laboratories for high precision measurements (e.g., interferometry) or in the field of ultrasonic sensing to amplify signal to noise ratio.…”