Damping and nonlinearity in elastic metamaterials: Treatment and effects

Abstract

Locally resonant acoustic/elastic metamaterials have been the focus of extensive research efforts in recent years due to their attractive dynamical characteristics, such as the possibility of exhibiting subwavelength bandgaps. In this work, we present rigorous formulations for the treatment of damping (e.g., viscous/viscoelastic) and nonlinearity (e.g., geometric/material) in the analysis of elastic wave propagation in elastic metamaterials. In the damping case, we use a generalized form of Bloch's theorem to obtain the dispersion and dissipation factors for freely propagating elastic waves. In the nonlinear case, we combine the standard transfer matrix with an exact formulation we have recently developed for finite-strain elastic waves in a homogeneous medium to obtain the band structure of a 1D elastic metamaterial. Our analysis sheds light on the effects of damping and nonlinearity on the dispersive characteristics in the presence of local resonance.