Discrete breathers in a mechanical metamaterial

TL;DR

This paper investigates discrete breather solutions in a mechanical metamaterial modeled as a chain of rigid units connected by hinges, revealing multiple stable and bifurcating localized oscillations through numerical analysis.

Contribution

It identifies parameter regimes for discrete breathers in a mechanical metamaterial and analyzes their stability and bifurcations, providing a foundation for experimental exploration.

Findings

Discrete breathers exist within specific parameter regimes.

Multiple bifurcation mechanisms affect breather stability.

Numerical stability analysis supports potential experimental observation.

Abstract

We consider a previously experimentally realized discrete model that describes a mechanical metamaterial consisting of a chain of pairs of rigid units connected by flexible hinges. Upon analyzing the linear band structure of the model, we identify parameter regimes in which this system may possess discrete breather solutions with frequencies inside the gap between optical and acoustic dispersion bands. We compute numerically exact solutions of this type for several different parameter regimes and investigate their properties and stability. Our findings demonstrate that upon appropriate parameter tuning within experimentally tractable ranges, the system exhibits a plethora of discrete breathers, with multiple branches of solutions that feature period-doubling and symmetry-breaking bifurcations, in addition to other mechanisms of stability change such as saddle-center and Hamiltonian Hopf bifurcations. The relevant stability analysis is corroborated by direct numerical computations examining the dynamical properties of the system and paving the way for potential further experimental exploration of this rich nonlinear dynamical lattice setting.