Discrete breathers in a mechanical metamaterial

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.

References in corpus (18)

• Discrete breathers in nonlinear lattices: Experimental detection in a Josephson array
• Observation of breathers in Josephson ladders
• Discrete Breathers in One-Dimensional Diatomic Granular Crystals
• Propagation of pop ups in kirigami shells
• Discrete breathers in a forced-damped array of coupled pendula: Modeling, Computation and Experiment
• Optical manipulation of intrinsic localized vibrational energy in cantilever arrays
• Discrete soliton mobility in two-dimensional waveguide arrays with saturable nonlinearity
• Formation of rarefaction waves in origami-based metamaterials
• Stability of topological edge states under strong nonlinear effects
• Multistable Solitons in Higher-Dimensional Cubic-Quintic Nonlinear Schroedinger Lattices
• Nonlinear waves in flexible mechanical metamaterials
• Damped-Driven Granular Crystals: An Ideal Playground for Dark Breathers and Multibreathers
• Nonlinear localized modes in two-dimensional electrical lattices
• Discrete breathers in a nonlinear electric line: Modeling, Computation and Experiment
• Bright and dark breathers in Fermi-Pasta-Ulam lattices
• Snaking and isolas of localised states in bistable discrete lattices
• Energy criterion for the spectral stability of discrete breathers
• A Unifying Perspective: Solitary Traveling Waves As Discrete Breathers And Energy Criteria For Their Stability