Periodic and chaotic oscillation of a parametrically excited viscoelastic moving belt with 1:3 internal resonance
黏弹性传动带1:3内共振时的周期和混沌运动

In this paper, the bifurcations of periodic solutions and chaotic dynamics for a parametrically excited viscoelastic moving belt with 1:3 internal resonance are investigated for the first time. The external damping and the internal damping of the material for viscoelastic moving belt are considered simultaneously. First, the nonlinear equation of planar motion for viscoelastic moving belt with the external damping is established. The Kelvin viscoelastic model is adopted to describe the relation between the stress and strain for viscoelastic material. Then, the transverse nonlinear oscillations of viscoelastic moving belt are considered. The method of multiple scales and the Galerkin approach are applied directly to the partial differential governing equation of viscoelastic moving belt to obtain the averaged equations under the case of 1:3 internal resonance and primary parametric resonance of the nth mode. Finally, numerical simulation method is used to investigated the bifurcations of periodic solutions and chaotic dynamics for viscoelastic moving belt. The chaotic motions are found under the cases of different parameters. The results of numerical simulation demonstrate that there exist periodic, 2-periodic, 3-periodic, 5-periodic and quasiperiodic responses and chaotic motions in viscoelastic moving belt.