Periodic and chaotic oscillations out of plane for viscoelastic axially moving beam

In this paper, periodic and chaotic oscillation out of plane are investigated for viscoelastic axially moving beam. The Kelvin viscoelastic model is chosen to describe the viscoelastic property of the beam material. Firstly, the nonlinear governing equations of out-of-plane motion are established by using the Hamilton's principle. Then, based on three-term Galerkin's discretization, the governing equations of motion are simplified to ordinary differential equations with six-degrees-of-freedom. The bifurcation diagram and phase portraits are given to capture the system's dynamical behavior. From numerical simulations, it is indicated that the periodic, quasi-periodic and chaotic motions occur in the out-of-plane vibrations of the axially accelerating viscoelastic beam.