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arXiv · 2508.19091

Nonlinear oscillations of strings and beams

Filip Ficek·Maciej Maliborski
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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.

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Filip Ficek, Maciej Maliborski. 2025-08-26. Nonlinear oscillations of strings and beams. https://arxiv.org/abs/2508.19091

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