Bifurcations and Chaos in a Cantilever Beam Vibration Model with Small Damping and Periodic Forced Terms

For the cantilever beam vibration model with small damping and forced terms, under some special parameter conditions, the corresponding unperturbed system can be described by a planar dynamical system. In this paper, by using the dynamical system method to analyze the unperturbed differential system and find bifurcations from the corresponding phase portraits, the dynamical behavior can be derived. Exact explicit homoclinic and heteroclinic solutions, and periodic solution families can be found. For the periodic perturbation system, the chaotic behavior of system is revealed. Numerical simulations are carried out to illustrate the theoretical results.