Bridging-Coupling Phenomenon in Linear Elastic Metamaterials by Exploiting Locally Resonant Metachain Isomers

Abstract

Elastic and acoustic metamaterials are man-made structures designed to control and manipulate waves through band gaps. The generalized bandwidth of metamaterials with locally resonant (LR) band gaps is usually narrow, limiting their applications in noise and vibration control. On the other hand, nonlinear metamaterials with dipolar resonances can present a broad chaotic band with low amplitude resonances due to bridging coupling, which is only observed under sufficiently large excitation amplitudes. In this work, we show that bridging-coupling phenomenon can also be observed in linear metamaterials with dipolar resonance, producing a special pass band with low amplitude resonances at low frequencies without excitation amplitude dependence. Such phenomenon emerges in a modified resonant metachain with zigzag interconnections and is based on the isomerism of traditional metamaterials. Although this modified isomer preserves the static stiffness and mass density (i.e., static performance) of the original metamaterial, its dispersive behavior presents interesting properties (i.e., branches with negative mass features and overlapping of opposite group velocity), resulting in an overall negative effective mass between the LR band gaps that is responsible for the remote interaction and the enhanced wave performance. In addition to the theoretical discussions, the bridging coupling is experimentally observed in a three-dimensional printed elastic metamaterial rod supporting longitudinal waves. The design can be extended to elastic bending, acoustic and electromechanical media, as well as to systems with periodicity in two and three dimensions (i.e., plates and solids). Therefore, the findings of this work open avenues to investigate the bridging-coupling phenomenon in linear systems as well as to explore the properties of metamaterial isomers.