Validation of FEM models based on Carrera Unified Formulation for the parametric characterization of composite metamaterials

Abstract

This work focuses on the study of composite metamaterials to be employed as possible lightweight insulation systems for noise and vibrations. In particular, the dispersion relations are derived by applying the Bloch-Floquet theory to the unit cell of the periodic microstructure. Advanced beam finite elements based on Carrera Unified Formulation are here extended, for the first time, to the dynamic characterization of these materials. Moreover, transmission curves are computed to validate the band gaps encountered in the analysis of dispersion behavior. The finite element model is first assessed by evaluating the dispersion behavior of some metamaterial configurations proposed in the literature. Finally, the model is applied to the parametric characterization of a composite metamaterial made of a melamine foam matrix and periodic distribution of cylindrical aluminium inclusions. The results show that it is possible to tune the band gaps of the metamaterial to lower frequencies by simply varying the dimensions of the unit cell and keeping constant its equivalent density.