Chinese Journal of Theoretical and Applied Mechani ›› 2004, Vol. 36 ›› Issue (4): 443-454.DOI: 10.6052/0459-1879-2004-4-2003-369
• Research paper •
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 $n$th 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.
viscoelastic moving belt,parametric excitation,internal resonance, chaotic dynamics
,,. Periodic and chaotic oscillation of a parametrically excited viscoelastic moving belt with 1:3 internal resonance[J]. Chinese Journal of Theoretical and Applied Mechani, 2004, 36(4): 443-454.
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