Periodic Solutions to Nonlinear Euler-Bernoulli Beam Equations

2018/04/10 by Bochao Chen, Yixian Gao, Chen, Bochao +3
Computer Science · Physics and Astronomy · #35B10 #35L72 #58C15 #58J45 #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1804.03300

openalex publication_date 2018/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 (ε,ω) in a Cantor set with asymptotically full measure as ε→0.

Citations

• Newton's method and periodic solutions of nonlinear wave equations
• Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory

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