Nonlinear Coupled Planar Forced Vibrations of Axially Moving Beams in the Supercritical Regimes

Steady-state periodic responses of nonlinear coupled planar vibrations are investigated for axially moving beams in the supercritical transport speed ranges. The forced vibration is assumed to be simple harmonic. The straight equilibrium configuration bifurcates in multiple equilibrium positions in the supercritical regime. The finite difference schemes are developed to calculate the non -trivial static equilibrium and the steady-state response under simple boundary conditions. Based on the time series, the steady-state transverse amplitudes of nonlinear planar vibrations are recorded with changing load frequencies. A resonance exists if the external load frequency approaches the fundamental frequency. The effects of material parameters and vibration amplitude on the resonance are investigated. The coupled planar model can be reduced to two nonlinear models on transverse vibrations, namely an integro-partial-differential equation and a partial -differential one. Numerical examples display the comparison among the three models.