Clamped seismic metamaterials: Ultra-low broad frequency stop-bands
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Published Version
Author(s)
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.
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.
Date Issued
2017-06-16
Date Acceptance
2017-04-20
Citation
New Journal of Physics, 2017, 9
ISSN
1367-2630
Publisher
IOP Publishing
Journal / Book Title
New Journal of Physics
Volume
9
Copyright Statement
© 2017 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Original content from this
work may be used under
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Commons Attribution 3.0
licence (https://creativecommons.org/licenses/by/3.0/).
Any further distribution of
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attribution to the
author(s) and the title of
the work, journal citation
and DOI.
work may be used under
the terms of the Creative
Commons Attribution 3.0
licence (https://creativecommons.org/licenses/by/3.0/).
Any further distribution of
this work must maintain
attribution to the
author(s) and the title of
the work, journal citation
and DOI.
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/L024926/1
Subjects
Science & Technology
Physical Sciences
Physics, Multidisciplinary
Physics
phononic crystal
mechanical metamaterial
seismic waves
PHOTONIC CRYSTALS
PERIODIC MEDIA
FLEXURAL WAVES
ELASTIC-WAVES
HOMOGENIZATION
ATTENUATION
PROPAGATION
PHYSICS
ARRAY
GAPS
physics.class-ph
Fluids & Plasmas
02 Physical Sciences