Sound attenuation performances of a duct silencer made of a metamaterial composed of a set of poroelastic lamellas, are investigated numerically and experimentally. The lamella arrangement is designed so that skeleton elastic resonances appear at low frequency. In addition, the air gap between the lamellas induces pressure diffusion effects commonly encountered in highly contrasted double porosity media. The configuration of the silencer also exhibits strong anisotropy. A 3D finite element model of the silencer has been developed in order to identify the different mechanisms taking place in the silencer. Numerical results are shown to match well with experimental data for different lamella orientations. By exploiting the geometrical periodicity of the silencer, a Bloch waves analysis is realized and a parametric study is conducted. This reveals strong model dispersion and interaction due to lamella elastic resonances. It is shown that certain design parameters can be tuned in order to achieve large attenuation and absorption at low frequency.