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arXiv · 2001.05693

Periodic solutions of a semilinear Euler-Bernoulli beam equation with variable coefficients

Hui Wei·Shuguan Ji
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Abstract

This paper is devoted to the study of periodic solutions for a semilinear Euler-Bernoulli beam equation with variable coefficients. Such mathematical model may be described the infinitesimal, free, undamped in-plane bending vibrations of a thin straight elastic beam. When the frequency $\omega =\frac{2\pi}{T}$ is rational, some properties of the beam operator with variable coefficients are investigated. We obtain the existence of periodic solutions when the nonlinear term is monotone and bounded.

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Hui Wei, Shuguan Ji. 2020-01-16. Periodic solutions of a semilinear Euler-Bernoulli beam equation with variable coefficients. https://doi.org/10.1016/j.cnsns.2021.105756

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