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The dispersion curves of a cluster of closely spaced rods supported by a thin plate are characterised by subwavelength bandgaps and slow group velocities induced by local resonance effects. A recent analytical study [Williams, Roux, Rupin, and Kuperman (2015). Phys. Rev. B 91, 104307], has shown how the slow velocity branch depends, amongst other parameters, on the height of the rods that make up the cluster. Such metamaterial, offering easy-to-tune spatial velocity gradients, is a perfect candidate for building gradient index lenses such as Luneburg, Maxwell, and 90°rotating. Here theoretical results are combined with numerical simulations to design and test metalenses for flexural waves. The lenses are obtained by tuning the height of the cluster of rods such that they provide the required refractive index profile. Snapshots and videos from three-dimensional numerical simulations in a narrow band centered at ~4 kHz are used to analyse the performances of three types of gradient index metalens (Luneburg, Maxwell, and 90° rotating). [ABSTRACT FROM AUTHOR]

This paper deals with the numerical design of a directional invisibility cloak for backward scattered elastic waves propagating in a thin plate (A0 Lamb waves). The directional cloak is based on a set of resonating beams that are attached perpendicular to the plate and are arranged at a sub-wavelength scale in ten concentric rings. The exotic effective properties of this locally resonant metamaterial ensure coexistence of bandgaps and directional cloaking for certain beam configurations over a large frequency band. The best directional cloaking was obtained when the resonators' length decreases from the central to the outermost ring. In this case, flexural waves experience a vanishing index of refraction when they cross the outer layers, leading to a frequency bandgap that protects the central part of the cloak. Numerical simulation shows that there is no back-scattering in these configurations. These results might have applications in the design of seismic-wave protection devices. [ABSTRACT FROM AUTHOR]

Deep sub-wavelength focusing has been demonstrated for locally resonant metamaterials using electromagnetic and acoustic waves. The elastic equivalents of such objects are made of sub-wavelength resonating beams fixed to a two-dimensional plate, as presented here. Independent of a random or regular arrangement of the resonators, the metamaterial shows large bandgaps that are independent of the incident wave direction. Numerical simulations demonstrate that the insertion of a defect in the layout, as a shorter resonator, creates strong amplification of the wave-field on the defect. This energy trapping, which is localized on a spatial scale that is much smaller than the wavelength in the two-dimensional plate, leads to a >1 factor in terms of the local density of energy. [ABSTRACT FROM AUTHOR]

Cross-correlations of ambient noise averaged at two receivers lead to the reconstruction of the two-point Green's function, provided that the wave-field is uniform azimuthally, and also temporally and spatially uncorrelated. This condition depends on the spatial distribution of the sources and the presence of heterogeneities that act as uncorrelated secondary sources. This study aims to evaluate the relative contributions of source distribution and medium complexity in the two-point cross-correlations by means of numerical simulations and laboratory experiments in a finite-size reverberant two-dimensional (2D) plate. The experiments show that the fit between the cross-correlation and the 2D Green's function depends strongly on the nature of the source used to excite the plate. A turbulent air-jet produces a spatially uncorrelated acoustic field that rapidly builds up the Green's function. On the other hand, extracting the Green's function from cross-correlations of point-like sources requires more realizations and long recordings to balance the effect of the most energetic first arrivals. When the Green's function involves other arrivals than the direct wave, numerical simulations confirm the better Green's function reconstruction with a spatially uniform source distribution than the typical contour-like source distribution surrounding the receivers that systematically gives rise to spurious phases. [ABSTRACT FROM AUTHOR]