Numerical investigation on 2D metamaterial under normal incidence

Abstract

Investigations in solid-state physics show that metamaterials, a kind of periodic material, can produce a band of frequency gap. When a sonic wave’s frequency falls into this frequency gap, it cannot propagate. Enlightened by the concept of frequency gap, researchers recently investigated various metamaterials. The search for bandgap(s) is critical in such innovations. The present letter presents the analysis of the band of frequency gap(s) for two and three-component systems as 2D period materials using the Finite Element Method. The investigation highlights the influence of geometrical parameters on the bandgap. Modelled metamaterial uses a core of aluminium, a coating of natural rubber and a matrix of air. For the lattice constant’s specified value, with the core’s increasing size, the bandgap shows to increase. The general effect of the coating leads to the flattening of the dispersion curve. For the square lattice and circular core, the bandgap appears around a net core size (with and without coating) of around 30%–32% of the lattice constant. Multiple frequency bandgaps appear of substantial sizes at the core’s threshold size, that is, when the core’s net radius is equal to half of the lattice constant. The softer material coating is found as a potential alternative to tune and control acoustic metamaterials. With a three-component system, bandgaps appear comparatively at significantly lower frequencies. Lower edge frequencies for such bandgaps are found to be independent of the core and coating size.