Nonlinear oscillations of strings and beams

Filip Ficek; Maciej Maliborski

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Nonlinear oscillations of strings and beams

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arxiv 2508.19091 v1 pith:FL6CYJCA submitted 2025-08-26 math-ph math.APmath.MPnlin.PS

Nonlinear oscillations of strings and beams

Filip Ficek , Maciej Maliborski This is my paper

classification math-ph math.APmath.MPnlin.PS

keywords nonlinearsolutionsclassanalysisbeambeamscomplexcompositions

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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.

Nonlinear oscillations of strings and beams

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