Clamped seismic metamaterials: Ultra-low broad frequency stop-bands - Achaoui,Y; Antonakakis,T; Brule,S; Craster,RV; Enoch,S; Guenneau,S (New Journal of Physics, 2017)
The regularity of earthquakes, their destructive power, and the nuisance of ground vibration in urbanenvironments, all motivate designs of defence structures to lessen the impact of seismic and groundvibration waves on buildings. Low frequency waves, in the range 1–10 Hz for earthquakes and up to afew tens of Hz for vibrations generated by human activities, cause a large amount of damage, orinconvenience; depending on the geological conditions they can travel considerable distances andmay match the resonant fundamental frequency of buildings. The ultimate aim of any seismicmetamaterial, or any other seismic shield, is to protect over this entire range of frequencies; the longwavelengths involved, and low frequency, have meant this has been unachievable to date. Notably thisis scalable and the effects also hold for smaller devices in ultrasonics. There are three approaches toobtaining shielding effects: bragg scattering, locally resonant sub-wavelength inclusions and zerofrequencystop-band media. The former two have been explored, but the latter has not and isexamined here. Elastic flexural waves, applicable in the mechanical vibrations of thin elastic plates, canbe designed to have a broad zero-frequency stop-band using a periodic array of very small clampedcircles. Inspired by this experimental and theoretical observation, all be it in a situation far removedfrom seismic waves, we demonstrate that it is possible to achieve elastic surface (Rayleigh)wavereflectors at very large wavelengths in structured soils modelled as a fully elastic layer periodicallyclamped to bedrock. We identify zero frequency stop-bands that only exist in the limit of columns ofconcrete clamped at their base to the bedrock. In a realistic configuration of a sedimentary basin 15 mdeep we observe a zero frequency stop-band covering a broad frequency range of 0–30 Hz.