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Multi-pulse homoclinic orbits and chaotic dynamics in motion of parametrically excited viscoelastic moving belt. (English) Zbl 1401.70012

Summary: In this paper, the multi-pulse homoclinic orbits and chaotic dynamics of parametrically excited viscoelastic moving belt are studied in detail. Using Kelvin-type viscoelastic constitutive law, the equations of motion for viscoelastic moving belt with external damping and parametric excitation are determined. The four-dimensional averaged equation under the case of \(1:1\) internal resonance and primary parametric resonance is obtained by directly using the method of multiple scales and Galerkin’s approach to the partial differential governing equation of viscoelastic moving belt. From the averaged equations obtained here, the theory of normal form is used to give the explicit expressions of normal form with a double zero and a pair of pure imaginary eigenvalues. Based on the normal form, the energy-phase method is employed to analyze the global bifurcations and chaotic dynamics in parametrically excited viscoelastic moving belt. The global bifurcation analysis indicates that there exist the homoclinic bifurcations and the Silnikov type multi-pulse homoclinic orbits in the averaged equation. The results obtained above mean the existence of the chaos for the Smale horseshoe sense in motion of parametrically excited viscoelastic moving belt. The chaotic motions of viscoelastic moving belts are also found by using numerical simulation.

MSC:

70E55 Dynamics of multibody systems
70K40 Forced motions for nonlinear problems in mechanics
74D05 Linear constitutive equations for materials with memory
37N15 Dynamical systems in solid mechanics
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