Résumé: © 2019 Acoustical Society of America. An accurate and numerically inexpensive method is presented to calculate the reflection of in-plane waves at the free surface of an elastic substrate supporting a periodic array of plates. The method is based on the expansions of the elastic fields on the pseudo-periodic modes in the substrate and on the Lamb modes in the plates. These expansions involve unknown amplitudes which are determined by simple matrix inversion when accounting for the boundary conditions at the surface of the substrate and at the free edges of the plates. Exemplifying results are reported in a wide range of frequency covering two resonances of the plates which are analyzed: a flexural resonance of slender bodies and the quasi-resonance of the so-called edge mode. The convergence of the method is inspected quantitatively; it is shown that it is good in view of the fact that the stress is singular at the corners of the plates in contact with the substrate. In particular, the scattering coefficients converge as 1/N s 3/2 with N s the truncation of the expansions.

Résumé: © 2019 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft. The human ear is a fascinating sensor, capable of detecting pressures over ten octaves of frequency and twelve orders of magnitudes. Here, following a biophysical model, we demonstrate experimentally that the physics of a living cochlea can be emulated by an active one-dimensional acoustic metamaterial. The latter solely consists on a set of subwavelength active acoustic resonators, coupled to a main propagating waveguide. By introducing a gradient in the resonators' properties, we establish an experimental set-up which mimics the dynamical responses of both the dead and the living cochleae: The cochlear tonotopy as well as the low-Amplitude sound amplifier are reproduced.