Discrete Breathers in One- and Two-Dimensional Mechanical Lattices
Publication Date
July 31, 2025
Creator
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 Schrödinger (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.
Item Type
ethesis
Thesis Type
PhD
Supervisors
Subjects (LC)
Associated Schools / Departments
School of Mathematical Sciences (UK)
eprints ID
81310
UoN Repository URI
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Name
Almarashi, Reem, 20249229, Corrected Submission.pdf
Type
Full-text
Description
Examined
Size
29.71 MB
Format
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