Homogenization and free-vibration analysis of elastic metamaterial plates by Carrera Unified Formulation finite elements

This work focuses on the assessment of a novel so-called “homogenization method” allowing to transform a heterogeneous material with inclusions or holes into an equivalent homogeneous material with equal mechanical behavior. The aim is to avoid meshing holes of the real material in finite-element codes, thus improving computation time for further analysis of the material. Typical periodic structure of passive acoustic metamaterial plates is considered here, with inclusions/holes that should improve the acoustic performances in the low-frequency range. The three-dimensional homogenization method, based on Carrera unified formulation (CUF) [E. Carrera, M. Cinefra, M. Petrolo, and E. Zappino. Finite Element Analysis of Structures through Unified Formulation. John Wiley & Sons, 2014] and Mechanics of Structure Genome, is assessed for a perforated plate made of a linear elastic material with periodic arrangement of holes. Different configurations of the metamaterial plate are considered, changing the number of the holes. The results obtained from the free-vibration analysis of the homogenized plates, performed by higher-order two-dimensional models contained in CUF, are compared with ABAQUS results and both numerical and experimental results provided in literature.