Absorption of a rigid frame porous layer with periodic circular inclusions backed by a periodic grating

The acoustic properties of a periodic rigid frame porous layer with multiple irregularities in the rigid backing and embedded rigid circular inclusions are investigated theoretically and numerically. The theoretical representation of the sound field in the structure is obtained using a combination of multipole method that accounts for the periodic inclusions and multi-modal method that accounts for the multiple irregularities of the rigid backing. The theoretical model is validated against a finite element method. The predictions show that the acoustic response of this structure exhibits quasi-total, high absorption peaks at low frequencies which are below the frequency of the quarter-wavelength resonance typical for a flat homogeneous porous layer backed by a rigid plate. This result is explained by excitation of additional modes in the porous layer and by a complex interaction between various acoustic modes. These modes relate to the resonances associated with the presence of a profiled rigid backing and rigid inclusions in the porous layer.