On the unique features of mechanical metamaterials with nonlinear local oscillators

Abstract

Over the last two decades, metamaterials have attracted a high number of researches motivated by the possibility of designing structures capable of manipulating wave propagation. The basic mechanism underlying the behavior of mechanical metamaterials is their negative effective dynamic parameters (mass and/or stiffness). Within the framework of mechanical metamaterials, most of the developments up to now have considered linear material behavior only. There is a natural need to understand the effect of nonlinear material behavior on the wave propagation through such engineered composites. In this paper, the dynamic behavior of a discrete lattice system composed of a series of nonlinear local resonators is investigated. By making use of the harmonic balance method, approximating dispersion relations are derived. Unlike previous works, super/sub-harmonic generation has been considered and revealed new phenomenon: the possibility of generating multiple transmission dips. The analysis also showed the tunability and multistability features of the system. The semi-analytical predictions were verified with direct numerical simulations.