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arXiv · 1804.03300

Periodic Solutions to Nonlinear Euler-Bernoulli Beam Equations

Bochao Chen·Yixian Gao·Yong Li
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Abstract

Bending vibrations of thin beams and plates may be described by nonlinear Euler-Bernoulli beam equations with $x$-dependent coefficients. In this paper we investigate existence of families of time-periodic solutions to such a model using Lyapunov-Schmidt reduction and a differentiable Nash-Moser iteration scheme. The results hold for all parameters $(\epsilon,\omega)$ in a Cantor set with asymptotically full measure as $\epsilon\rightarrow0$.

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Bochao Chen, Yixian Gao, Yong Li. 2018-04-10. Periodic Solutions to Nonlinear Euler-Bernoulli Beam Equations. https://arxiv.org/abs/1804.03300

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