Nonlinear oscillations of strings and beams
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914006853222400 |
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| author | Ficek, Filip Maliborski, Maciej |
| author_facet | Ficek, Filip Maliborski, Maciej |
| contents | We investigate the time-periodic solutions to the nonlinear wave and beam equations and uncover their intricate, fractal-like structure. In particular, we identify a new class of large-energy solutions with complex mode compositions and propose a systematic framework for their analysis. A Floquet stability study reveals that this class contains solutions that are linearly stable, suggesting that they may play a significant role in the nonlinear dynamics of the systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19091 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear oscillations of strings and beams Ficek, Filip Maliborski, Maciej Mathematical Physics Analysis of PDEs Pattern Formation and Solitons We investigate the time-periodic solutions to the nonlinear wave and beam equations and uncover their intricate, fractal-like structure. In particular, we identify a new class of large-energy solutions with complex mode compositions and propose a systematic framework for their analysis. A Floquet stability study reveals that this class contains solutions that are linearly stable, suggesting that they may play a significant role in the nonlinear dynamics of the systems. |
| title | Nonlinear oscillations of strings and beams |
| topic | Mathematical Physics Analysis of PDEs Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2508.19091 |