The numerical study of the nonlinear dynamics of a light, axially moving string

The vibration characteristics of a light axially moving band are investigated by a numerical study in the subcritical and supercritical speed ranges. Equations of motion for the geometrically nonlinear axially moving string are formulated using Hamiltonʹs principle and discretized by the finite element method. The periodic nonlinear problem for the string is solved by the Fourier–Galerkin–Newton (FGN) method. The nonlinear dynamic behaviour of an axially moving band is examined through the dependences between the fundamental frequency, axial velocity and vibration amplitude resulting from nonlinear free vibration. In general, the behaviour of the nonlinear axially moving string is similar to that of a nonlinear beam, the most notable differences being the fact that the string does not undergo bifurcation from a straight configuration to curved equilibrium states in a supercritical transport speed regime, nor does the equilibrium state remain straight.