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Numerical simulations

Barrier Unit-Cell

Schematics of the metabarrier unit cell


  • 2D unit-cell of the barrier is built based on the simplified design approach of the resonators.
  • Bloch-Floquet boundary conditions are applied at the sides of the soil.
  • Dispersion curve of the barrier unit-cell is obtained. 
  • No evidence of complete band-gaps due to the presence of multiple surface waves is observed.

  • The resonator in the soilshiftsits frequency to 45 Hz (the soil acts as an additional soft spring).

FE model schematics

Schematics of the full 2D FE model


  • Full 2D FE model is built based on the unit-cell.
  • Ricker wavelet excites the model at the central frequency of 50 Hz to generates surface waves. 
  • Vertical nodal displacements of 11 equally distributed points along the output range are taken, FFTs are calculated and averaged and then each averaged spectra is normalized by the averaged spectra of “reference soil model - RSM”.
Barrier Performance

Barrier performance: simplified resonators vs dead masses 


  • Resonators are modeled based on the simplified design approach.
  • Barrier performance is compared to the soil reference model.
  • The introduction of the resonators induces a peak of attenuation around their resonance frequency 
  • Dead masses added on the soil top surface do not induce significant attenuation