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

## TL;DR

This paper demonstrates that structured soils with periodically clamped columns can create broad zero-frequency stop-bands, effectively reflecting seismic waves in the 0-30 Hz range, offering a new approach to seismic wave mitigation.

## Contribution

It introduces a novel seismic metamaterial design using periodically clamped columns to achieve broad low-frequency stop-bands in soils.

## Key findings

- Zero frequency stop-bands exist with clamped columns.
- Broad stop-band from 0 to 30 Hz in a 15-meter-deep basin.
- Effective seismic wave reflection in the targeted frequency range.

## 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.