Zeighami, Farhad
(2016)

*Sub-wavelength resonators as seismic Rayleigh waves shield.*
[Laurea magistrale], Università di Bologna, Corso di Studio in

Civil engineering [LM-DM270], Documento full-text non disponibile

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## Abstract

We explore the thesis that tall structures can be protected by means of seismic metamaterials. Seismic metamaterials can be built as some elements are created over soil layer with different shapes, dimensions, patterns and from different materials. Resonances in these elements are acting as locally resonant metamaterials for Rayleigh surface waves in the geophysics context. Analytically we proved that if we put infinite chain of SDOF resonator over the soil layer as an elastic, homogeneous and isotropic material, vertical component of Rayleigh wave, longitudinal resonance of oscillators will couple with each other, they would create a Rayleigh bandgap frequency, and wave will experience attenuation before it reaches the structure.
As it is impossible to use infinite chain of resonators over soil layer, we considered finite number of resonators throughout our simulations. Analytical work is interpreted using finite element simulations that demonstrates the observed attenuation is due to bandgaps when oscillators are arranged at sub-wavelength scale with respect to the incident Rayleigh wave. For wavelength less than 5 meters, the resulting bandgaps are remarkably large and strongly attenuating when impedance of oscillators matches impedance of soil. Since longitudinal resonance of SDOF resonator are proportional to its length inversely, a formed array of resonators that attenuates Rayleigh waves at frequency ≤10 Hz could be designed starting from vertical pillars coupled to the ground. Optimum number of vertical pillars and their interval spacing called effective area of resonators are investigated. For 10 pillars with effective area of 1 meter and resonance frequency of 4.9 Hz, bandgap frequency causes attenuation and a sinusoidal impulsive force illustrate wave steering down phenomena. Simulation results proved analytical findings of this work.

Abstract

We explore the thesis that tall structures can be protected by means of seismic metamaterials. Seismic metamaterials can be built as some elements are created over soil layer with different shapes, dimensions, patterns and from different materials. Resonances in these elements are acting as locally resonant metamaterials for Rayleigh surface waves in the geophysics context. Analytically we proved that if we put infinite chain of SDOF resonator over the soil layer as an elastic, homogeneous and isotropic material, vertical component of Rayleigh wave, longitudinal resonance of oscillators will couple with each other, they would create a Rayleigh bandgap frequency, and wave will experience attenuation before it reaches the structure.
As it is impossible to use infinite chain of resonators over soil layer, we considered finite number of resonators throughout our simulations. Analytical work is interpreted using finite element simulations that demonstrates the observed attenuation is due to bandgaps when oscillators are arranged at sub-wavelength scale with respect to the incident Rayleigh wave. For wavelength less than 5 meters, the resulting bandgaps are remarkably large and strongly attenuating when impedance of oscillators matches impedance of soil. Since longitudinal resonance of SDOF resonator are proportional to its length inversely, a formed array of resonators that attenuates Rayleigh waves at frequency ≤10 Hz could be designed starting from vertical pillars coupled to the ground. Optimum number of vertical pillars and their interval spacing called effective area of resonators are investigated. For 10 pillars with effective area of 1 meter and resonance frequency of 4.9 Hz, bandgap frequency causes attenuation and a sinusoidal impulsive force illustrate wave steering down phenomena. Simulation results proved analytical findings of this work.

Tipologia del documento

Tesi di laurea
(Laurea magistrale)

Autore della tesi

Zeighami, Farhad

Relatore della tesi

Correlatore della tesi

Scuola

Corso di studio

Ordinamento Cds

DM270

Parole chiave

Seismic Metamaterial,Rayleigh wave,dispersion equation,bandgap frequency,Finite element modeling,sub-wavelength resonator,wave propagation

Data di discussione della Tesi

14 Luglio 2016

URI

## Altri metadati

Tipologia del documento

Tesi di laurea
(NON SPECIFICATO)

Autore della tesi

Zeighami, Farhad

Relatore della tesi

Correlatore della tesi

Scuola

Corso di studio

Ordinamento Cds

DM270

Parole chiave

Seismic Metamaterial,Rayleigh wave,dispersion equation,bandgap frequency,Finite element modeling,sub-wavelength resonator,wave propagation

Data di discussione della Tesi

14 Luglio 2016

URI

Gestione del documento: