Ti t l e S o u n d a b s o r p tio n a n d r efl e c tio n fro m a r e s o n a n t m e t a s u rf a c e : h o m o g e niz a tio n m o d el wi t h e x p e ri m e n t al v alid a tio n

This article presents a numerical optimization procedure of continuous gradient porous layer properties to achieve perfect absorption under normal incidence. This design tool is applied on a graded porous medium composed of a periodic arrangement of ordered unit cells allowing to link the effective acoustic properties to its geometry. The best microgeometry continuous gradient providing the optimal acoustic reflection and/or transmission is designed via a nonlinear conjugate gradient algorithm. The acoustic performances of the so-designed continuous graded material are discussed with respect to the optimized homogeneous, i.e. non-graded, and monotonically graded material. The numerical results show a shifting of the perfect absorption peak to lower frequencies or a widening of the perfect absorption frequency range for graded materials when compared to uniform ones. The results are validated experimentally on 3D-printed samples therefore confirming the relevance of such gradient along with the efficiency of the control of the entire design process.

S U M M A R YThe collective excitation of city structures by a seismic wavefield and the subsequent multiple Structure-Soil-Structure Interactions (SSSIs) between the buildings are usually disregarded in conventional seismology and earthquake engineering practice. The objective here is to qualify and quantify these complex multiple SSSIs through the design of an elementary study case, which serves as a benchmark for theoretical, numerical and experimental crossed-analysis. The experimental specimen consists of an idealized site-city setup with up to 37 anisotropic resonant structures arranged at the top surface of an elastic layer and in co-resonance with it. The experimental data from shaking table measurements is compared with the theoretical and numerical results provided respectively by an equivalent city-impedance model derived analytically from homogenization in the long-wavelength approximation and a model based on boundary elements. The signatures of the site-city interactions are identified in the frequency, time and space domain, and in particular consist of a frequency-dependent free/rigid switch in the surface condition at the city resonance, beatings in the records and the depolarization of the wavefield. A parametric study on the city density shows that multiple SSSIs among the city structures (five are sufficient) can have significant effects on both the seismic response of its implantation site and that of the buildings. Key parameters are provided to assess site-city interactions in the low seismic frequency range: They involve the mass and rigidity of the city compared to those of the soil and the damping of the building.Key words: Earthquake dynamics; Earthquake ground motions; Body waves; Seismic anisotropy; Site effects; Wave propagation. I N T RO D U C T I O NUrban and industrial areas require a particular attention in seismic analysis due to the concentrations of population, real estates, strategic public services and human activities having a large socioeconomical impact. However, the presence of the city is usually disregarded in conventional methods applied in seismology and earthquake engineering: The ground motion is supposed to result from the seismic source and substratum properties only, for example, Bonnefoy-Claudet et al. (2008), while the response of a structure to the ground motion is studied independently from the surrounding buildings, for example, Jennings & Bielak (1973). These standard approaches omit the effects of multiple soil-structures dynamic interactions on the seismic field and the buildings' response.While these approximations are reasonable in most cases, they are questionable in urban areas, where high-rise buildings, similar in height and design, are built closely from one another. Neighbouring buildings can exchange significant amounts of energy with each other, and form, with the soil, a fully coupled dynamic system that should be treated as a whole. The problem of mutual interactions between two buildings have been formulated initially by Luco & Contesse (19...