Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances.

Andrea Colombi,Sebastien Guenneau,Richard V Craster,Philippe Gueguen,Philippe Roux

doi:10.1038/srep19238

Abstract

We explore the thesis that resonances in trees result in forests acting as locally resonant metamaterials for Rayleigh surface waves in the geophysics context. A geophysical experiment demonstrates that a Rayleigh wave, propagating in soft sedimentary soil at frequencies lower than 150 Hz, experiences strong attenuation, when interacting with a forest, over two separate large frequency bands. This experiment is interpreted using finite element simulations that demonstrate the observed attenuation is due to bandgaps when the trees are arranged at the sub-wavelength scale with respect to the incident Rayleigh wave. The repetitive bandgaps are generated by the coupling of the successive longitudinal resonances of trees with the vertical component of the Rayleigh wave. For wavelengths down to 5 meters, the resulting bandgaps are remarkably large and strongly attenuating when the acoustic impedance of the trees matches the impedance of the soil. Since longitudinal resonances of a vertical resonator are inversely proportional to its length, a man-made engineered array of resonators that attenuates Rayleigh waves at frequency ≤10 Hz could be designed starting from vertical pillars coupled to the ground with longitudinal resonance ≤10 Hz.

Highlights

Previous experiments on geophysical scales using periodic structures, embedded in the ground[16,17] occur at frequencies too high (≫ 100 Hz) for practical seismic applications
Because of the deep sub-wavelength microstructure of locally resonant metamaterials, it is essential to explore the wavefield within the resonator array with spatio-temporal details that would require thousands of seismometers in the present geophysical configuration
The physics of the sub-wavelength structure is accurately analysed in this paper through time domain spectral element (SEM) simulations

Summary

Introduction

Previous experiments on geophysical scales using periodic structures, embedded in the ground[16,17] occur at frequencies too high (≫ 100 Hz) for practical seismic applications. [18], recently demonstrated the first metamaterial for surface wave control using vertical sub-wavelength boreholes, in a sedimentary soil, obtaining partial bandgaps and wavefield attenuation for frequency around 50 Hz. The laboratory experiment in the sonic regime with plate and rods of[13] implies that the attenuation capacity of vertical resonators could exceed those of boreholes. The usage of natural metamaterial may sound in conflict with the conventional definition of metamaterial as an artificially engineered object This concept is reminiscent of early works on negative refracting metamaterials developed to obtain perfect lenses[2,20]. The scalability in frequency of physical laws that underlie metamaterials is a well-established concept[21], and it is understandable that nature could offer examples of metamaterials from the nano to the meso-scale[22]

Methods

Results

Conclusion