Zener internal damping in modelling of axially moving viscoelastic beam with time-dependent tension

Non-linear vibrations of axially moving beam with time-dependent tension are investigated in this paper. The beam material is modelled as three-parameter Zener element. The Galerkin method and the fourth order Runge-Kutta method are used to solve the governing non-linear partial-differential equation. The effects of the transport speed, the tension perturbation amplitude and the internal damping on the dynamic behaviour of the system are numerically investigated. The Poincare maps and bifurcation diagrams are constructed to classify the vibrations. For small values of the transport speed and the amplitude of periodic perturbation the system is asymptotically stable with its response tending to zero. With the increase of parameters one can observe the coexistence of attractors. Regular and chaotic motion occur when the internal damping increases.