Sub-wavelength resonators as seismic Rayleigh waves shield

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.

Dispersion and energy relations in periodic chains and grids

In this study wave propagation, dispersion relations, and energy relations for linear elastic periodic systems are analyzed. In particular, the dispersion relations for monoatomic chain of infinite dimension are obtained analytically by writing the Block-type wave equation for a unit cell in order to capture the dynamic behavior for chains under prescribed vibration. By comparing the discretized model (mass-spring chain) with the solid bar system, the nonlinearity of the dispersion relation for chain indicates that the periodic lattice is dispersive in contrast to the continuous rod, which is non dispersive. Further investigations have been performed considering one-dimensional diatomic linear elastic mass-spring chain. The dispersion relations, energy velocity, and group velocity have been derived. At certain range of frequencies harmonic plane waves do not propagate in contrast with monoatomic chain. Also, since the diatomic chain considered is a linear elastic chain, both of the energy velocity and the group velocity are identical. As long as the linear elastic condition is considered the results show zero flux condition without residual energy. In addition, this paper shows that the diatomic chain dispersion relations are independent on the unit cell scheme. Finally, an extension for the study covers the dispersion and energy relations for 2D- grid system. The 2x2 grid system show a periodicity of the dispersion surface in the wavenumber domain. In addition, the symmetry of the surface can be exploited to identify an Irreducible Brillouin Zone (IBZ). Compact representations of the dispersion properties of multidimensional periodic systems are obtained by plotting frequency as the wave vector’s components vary along the boundary of the IBZ, which leads to a widely accepted and effective visualization of bandgaps and overall dispersion properties.

Impact of convective motions on pollutant dispersion in urban canyons: an analysis through RANS simulations

Since the majority of the population of the world lives in cities and that this number is expected to increase in the next years, one of the biggest challenges of the research is the determination of the risk deriving from high temperatures experienced in urban areas, together with improving responses to climate-related disasters, for example by introducing in the urban context vegetation or built infrastructures that can improve the air quality. In this work, we will investigate how different setups of the boundary and initial conditions set on an urban canyon generate different patterns of the dispersion of a pollutant. To do so we will exploit the low computational cost of Reynolds-Averaged Navier-Stokes (RANS) simulations to reproduce the dynamics of an infinite array of two-dimensional square urban canyons. A pollutant is released at the street level to mimic the presence of traffic. RANS simulations are run using the k-ɛ closure model and vertical profiles of significant variables of the urban canyon, namely the velocity, the turbulent kinetic energy, and the concentration, are represented. This is done using the open-source software OpenFOAM and modifying the standard solver simpleFoam to include the concentration equation and the temperature by introducing a buoyancy term in the governing equations. The results of the simulation are validated with experimental results and products of Large-Eddy Simulations (LES) from previous works showing that the simulation is able to reproduce all the quantities under examination with satisfactory accuracy. Moreover, this comparison shows that despite LES are known to be more accurate albeit more expensive, RANS simulations represent a reliable tool if a smaller computational cost is needed. Overall, this work exploits the low computational cost of RANS simulations to produce multiple scenarios useful to evaluate how the dispersion of a pollutant changes by a modification of key variables, such as the temperature.