Periodic and chaotic oscillation of a parametrically excited viscoelastic moving belt with 1:3 internal resonance

In this paper, the bifurcations of periodic solutions andchaotic dynamics for a parametrically excited viscoelastic moving belt with1:3 internal resonance are investigated for the first time. The externaldamping and the internal damping of the material for viscoelastic movingbelt are considered simultaneously. First, the nonlinear equation of planarmotion for viscoelastic moving belt with the external damping isestablished. The Kelvin viscoelastic model is adopted to describe therelation between the stress and strain for viscoelastic material. Then, thetransverse nonlinear oscillations of viscoelastic moving belt areconsidered. The method of multiple scales and the Galerkin approach areapplied directly to the partial differential governing equation ofviscoelastic moving belt to obtain the averaged equations under the case of1:3 internal resonance and primary parametric resonance of the nth mode.Finally, numerical simulation method is used to investigated thebifurcations of periodic solutions and chaotic dynamics for viscoelasticmoving belt. The chaotic motions are found under the cases of differentparameters. The results of numerical simulation demonstrate that there existperiodic, 2-periodic, 3-periodic, 5-periodic and quasiperiodic responses andchaotic motions in viscoelastic moving belt.