Clamped seismic metamaterials: Ultra-low broad frequency stop-bands

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Title: Clamped seismic metamaterials: Ultra-low broad frequency stop-bands
Authors: Achaoui, Y
Antonakakis, T
Brule, S
Craster, RV
Enoch, S
Guenneau, S
Item Type: Journal Article
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.
Issue Date: 16-Jun-2017
Date of Acceptance: 20-Apr-2017
ISSN: 1367-2630
Publisher: IOP Publishing
Journal / Book Title: New Journal of Physics
Volume: 19
Copyright Statement: © 2017 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence ( Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/L024926/1
Keywords: Science & Technology
Physical Sciences
Physics, Multidisciplinary
phononic crystal
mechanical metamaterial
seismic waves
Fluids & Plasmas
02 Physical Sciences
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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