Wave attenuation in viscoelastic hierarchical plates

Phononic crystals (PCs) are periodic structures obtained by the spatial arrangement of materials with contrasting properties, which can be designed to efficiently manipulate mechanical waves. Plate modeled using Mindlin–Reissner plate theory and have been extensively used analyze dispersion relations PCs. Although analysis propagating characteristics PCs may sufficient for simple elastic structures, analyzing evanescent wave behavior becomes fundamental if PC contains viscoelastic components. Another complication is that increasingly intricate material distributions in unit cell hierarchical configuration render calculation complex band structure (i.e., considering both waves) prohibitive due excessive computational workload. In this work, we propose a new extended plane expansion formulation compute thick plates arbitrary distribution containing constituents approximated Kelvin–Voigt model. We apply method investigate hierarchically structured either (i) hard purely matrix soft inclusions or (ii) inclusions. Our results show (i), an increase order leads weight reduction relatively preserved attenuation characteristics, including peaks locally resonant modes present decrease upon increasing viscosity levels. For (ii), changing implies opening gaps distinct frequency ranges, overall improved