Multiple Band-Gaps through the Coupling of Unit Cells from the Same Metamaterial: the Dual Cell method

Abstract

This study investigates how the coupling of two unit cells belonging to the same mechanical metamaterial into a dual unit cell configuration, can produce a new metamaterial with enhanced wave attenuation capabilities. For two metamaterials, two different unit cell coupling configurations are examined in 2D (side by side and chessboard), with particular emphasis on maintaining a plane crystallographic group of high symmetry, in order to simplify band structure calculations given the complexity of the geometry. It is shown that for specific configurations and choices of unit cell, multiple directional and/or omnidirectional band-gaps can appear, some of which can exhibit enhanced attenuation. The way in which these band-gaps emerge is described through applying the same procedure on 1D spring mass chains. Results support the idea that any band-gap metamaterial could have a much more efficient version which can be constructed purely from its own unit cells.