Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 17, Issue 5, Pages 1637-1660Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127407017963
Keywords
viscoelastic moving belt; higher-dimensional nonlinear system; parametric excitation; multiple internal resonance; multipulse chaos
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In this paper, higher-dimensional periodic and chaotic oscillations for a parametrically excited viscoelastic moving belt with multiple internal resonances are investigated for the first time. The external damping and internal damping of the material for the viscoelastic moving belt are considered simultaneously. First, the nonlinear governing equation of planar motion for the viscoelastic moving belt with the external damping is given. Then, the transverse nonlinear oscillations of the viscoelastic moving belt are considered. The method of multiple scales and the Galerkin approach are applied directly to the governing partial differential equation of motion for the viscoelastic moving belt to obtain an eight-dimensional averaged equation for the case of 1:2:3:4 internal resonances for the first-,the second-, the third- and the fourth-order modes and primary parametric resonance of the first-order mode. Finally, numerical method is used to investigate higher-dimensional periodic and chaotic motions of the viscoelastic moving belt. The results of numerical simulation demonstrate that there exist the period, period 2, period 4, multiple period and chaotic motions of the viscoelastic moving belt. The multipulse chaotic motions of the viscoelastic moving belt are observed from numerical simulations.
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