  Based on our previous work, we propose a homogenized model of acoustic waves
propagating through periodically perforated elastic plates with metamaterial
properties due to embedded arrays of soft elastic inclusions serving for
resonators. Such structures enable to suppress the acoustic transmission for
selected frequency bands. Homogenization of the vibro-acoustic fluid-structure
interaction problem in a 3D complex geometry of the transmission layer leads to
effective transmission conditions prescribed on the acoustic meta-surface
associated with the mid-plane of the Reissner-Mindlin plate. Asymptotic
analysis with respect to the layer thickness, proportional to the plate
thickness and to the perforation period, yields an implicit
Dirichlet-to-Neumann operator defined on the homogenized metasurface. An
efficient method is proposed for computing frequency-dependent effective
parameters involved in the homogenized model of the layer. These can change
their signs, thus modifying the acoustic impedance and the effective mass of
the metasurface. The global problem of the acoustic wave propagation in a
waveguide fitted with the plate is solved using the finite element method. The
homogenized interface allows for a significant reduction of the computational
model. Numerical illustrations are presented.
