  The acoustic properties of a porous sheet of medium resistivity backed by a
rigid plate in which are embedded a periodic set of circular inclusions is
investigated. Such a structure behaves like a multi-component diffraction
gratings. Numerical results show that this structure presents a quasi-total
absorption peak below the essential spectrum, i.e. below the frequence of the
fundamental quarter-wavelength resonance of the porous sheet in absence of
inclusions. This result is explained either by the excitation of a complex
trapped mode, or by the increase of viscous loss associated with a larger
velocity gradient inside the layer at the modified quarter-wavelength resonance
frequency. When more than one inclusion per spatial period are considered,
additional quasi-total frequency peak are observed. The numerical results as
calculated with the help of the mode-matching method described in the paper
agree those as calculated with the help of a Finite Element method.
