Dynamic homogenization of multi-layered lattice-like metamaterials with alternate chiral microstructure

Abstract

This paper presents a dynamic continualization technique for a multi-layer beam-lattice metamaterial with an alternating chiral microstructure, where each layer is reciprocally interconnected through the insertion of pins. The study analyzes the dispersive properties of the system and its potential applications as a meta-filter, highlighting how the enhanced continualization technique introduced can capture the dispersive properties of stratified systems with chiral geometry. This approach makes it possible to derive higher-order gradient-type continuum models that yield dispersion spectra close to those obtained through a discrete Lagrangian treatment, without encountering dynamic instability effects due to thermodynamic inconsistency. These aspects are further investigated through the presentation of application examples, specifically concerning a stratified tetrachiral waveguide. A key finding of the studied examples is related to the passive/active tunability of the system, specifically in relation to the stiffness of the pin which determines significant influences on the dispersion spectra. To complete the analysis, a further example is finally proposed in which the waveguide is subjected to harmonic excitation, revealing how variations in the parameters can affect wave polarizations.