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Vibrations of a beam can be described as an Euler-Bernoulli beam, or as a Rayleigh beam or as a Timoshenko beam. In this paper, we establish the existence of periodic solutions in time for a damped Rayleigh beam model with time delay, which is treated as a bifurcation parameter. The main proof is based on a Lyapunov-Schmidt reduction together with the classical implicit function theorem. Moreover, we give a sufficient condition for a direction of bifurcation.
}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2020-0015}, url = {http://global-sci.org/intro/article_detail/cmr/17850.html} }Vibrations of a beam can be described as an Euler-Bernoulli beam, or as a Rayleigh beam or as a Timoshenko beam. In this paper, we establish the existence of periodic solutions in time for a damped Rayleigh beam model with time delay, which is treated as a bifurcation parameter. The main proof is based on a Lyapunov-Schmidt reduction together with the classical implicit function theorem. Moreover, we give a sufficient condition for a direction of bifurcation.