Discrete Breathers in One- and Two-Dimensional Mechanical Lattices
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 unstabl...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
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2025
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| Online Access: | https://eprints.nottingham.ac.uk/81310/ |
| _version_ | 1848801313136050176 |
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| author | Almarashi, Reem |
| author_facet | Almarashi, Reem |
| author_sort | Almarashi, Reem |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T21:05:28Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-81310 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T21:05:28Z |
| publishDate | 2025 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-813102025-07-31T04:40:29Z https://eprints.nottingham.ac.uk/81310/ Discrete Breathers in One- and Two-Dimensional Mechanical Lattices Almarashi, Reem 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. 2025-07-31 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en https://eprints.nottingham.ac.uk/81310/1/Almarashi%2C%20Reem%2C%2020249229%2C%20Corrected%20Submission.pdf Almarashi, Reem (2025) Discrete Breathers in One- and Two-Dimensional Mechanical Lattices. PhD thesis, University of Nottingham. nonlinear systems lattices discrete breathers waves |
| spellingShingle | nonlinear systems lattices discrete breathers waves Almarashi, Reem Discrete Breathers in One- and Two-Dimensional Mechanical Lattices |
| title | Discrete Breathers in One- and Two-Dimensional Mechanical Lattices |
| title_full | Discrete Breathers in One- and Two-Dimensional Mechanical Lattices |
| title_fullStr | Discrete Breathers in One- and Two-Dimensional Mechanical Lattices |
| title_full_unstemmed | Discrete Breathers in One- and Two-Dimensional Mechanical Lattices |
| title_short | Discrete Breathers in One- and Two-Dimensional Mechanical Lattices |
| title_sort | discrete breathers in one- and two-dimensional mechanical lattices |
| topic | nonlinear systems lattices discrete breathers waves |
| url | https://eprints.nottingham.ac.uk/81310/ |