Nonlinear oscillations of strings and beams
Mathematical Physics
2025-08-27 v1 Analysis of PDEs
math.MP
Pattern Formation and Solitons
Abstract
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.
Cite
@article{arxiv.2508.19091,
title = {Nonlinear oscillations of strings and beams},
author = {Filip Ficek and Maciej Maliborski},
journal= {arXiv preprint arXiv:2508.19091},
year = {2025}
}
Comments
6 pages, 5 figures + Supplemental Material