Non-linear vibrations of an axially moving viscoelastic web with time-dependent tension

Non-linear vibrations of beam-like model of two-dimensional axially moving web with time-dependent tension have been investigated in this paper. The beam model material as the Kelvin–Voigt element is considered. The Galerkin method and the fourth-order Runge–Kutta method were 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 were numerically investigated. The Poincare maps have been 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 local pitchwork type bifurcation and the coexistence of attractors. For small values of internal damping chaotic motion occurs. Regular and chaotic motions occur when internal damping increases.