Discrete Breathers in One- and Two-Dimensional Mechanical Lattices

Abstract

In this thesis, we investigate discrete breathers in nonlinear mechanical lattices through numerical and asymptotic methods. First, in a one-dimensional mass in- mass Fermi-Pasta-Ulam-Tsingou (FPUT) chain with internal oscillators, we identify stable stationary breathers and long-lived weakly unstable stationary and moving breathers and breather kinks. Second, in two-dimensional hexagonal lattices, we use multiple scales analysis, we derive the equations governing wave propagation and reduce them to Nonlinear Schrodinger (NLS) equations. We identify the ellipticity condition and a focusing condition for the exist of fully localised NLS solutions in triangular geometries, and derive (2+1)-dimensional and coupled (2+1)-dimensional NLS subsystems in honeycomb structures. The latter arise from critical points of the dispersion relation and yield existence criteria for small-amplitude breathers. These results are relevant for predictive models for energy localisation in mechanical metamaterials as they link lattice symmetry, nonlinearity and breather stability.