Homogenization of the vibro–acoustic transmission on periodically perforated elastic plates with arrays of resonators

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