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.

References in corpus (6)

• Novel hyperbolic metamaterials based on multilayer graphene structures
• Seismic metasurfaces: Sub-wavelength resonators and Rayleigh wave interaction
• On occurrence of spectral edges for periodic operators inside the Brillouin zone
• Calculation and analysis of complex band structure in dispersive and dissipative two-dimensional photonic crystals
• Scattering problems in elastodynamics
• Unveiling Extreme Anisotropy in Elastic Structured Media

Cited by in corpus (14)

• Homogenization of quasiperiodic structures and two-scale cut-and-projection convergence
• Mitigation of seismic waves: metabarriers and metafoundations bench tested
• Design of tunable acoustic metamaterials with periodic piezoelectric microstructure
• Geometrically navigating topological platonic modes around gentle and sharp bends
• Ultra-thin Underwater Acoustic Metasurface with Multiply Resonant Units
• Omnidirectional flexural invisibility of multiple interacting voids in vibrating elastic plates
• Elastic three-dimensional metaframe for selective wave filtering and polarization control
• Scattering theory and cancellation of gravity-flexural waves of floating plates
• Regular sloshing modes in irregular cavities using metabathymetry
• Graded metasurface for enhanced sensing and energy harvesting
• Asymptotic modelling of phononic box crystals
• On the spectral asymptotics of waves in periodic media with Dirichlet or Neumann exclusions
• The influence of structure geometry and material on seismic metamaterial performance
• Elastic wave control beyond band-gaps: shaping the flow of waves in plates and half-spaces