Title: Clamped seismic metamaterials: Ultra-low broad 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 $1$ to $10$ 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.
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)
and body (pressure P and shear S) 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 meters deep we observe a zero frequency stop-band
covering a broad frequency range of $0$ to $30$ Hz.