Homogenized models of acoustic metainterfaces made of three-dimensional Helmholtz resonators

We investigate the behaviour of metainterfaces composed of three-dimensional subwavelength Helmholtz resonators (HRs), that are open at both ends and may have distinct neck geometries, using a homogenized model derived from a three-scale asymptotic approach. This model reduces such metainterfaces to homogenized boundary conditions that incorporate a resonant pressure field, providing a continuous representation of the discrete pressure field within the cavities that constitute the metasurface. Notable special cases include mirror-symmetric metainterfaces and metasurfaces that operate solely in reflection. The model, developed in the time domain, is validated and discussed in the harmonic regime through comparisons with direct numerical simulations.