Nonplanar Periodic and Chaotic Oscillation of an Axially Moving Viscoelastic Belt with One-to-One Internal Resonance

摘要

Nonplanar periodic and chaotic space oscillations of an axially moving viscoelastic belt with one-to-one internal resonance are investigated for the first time. The Kelvin viscoelastic model is introduced to describe the viscoelastic property of the belt material. The external damping and internal damping of the material for the axially moving viscoelastic belt are considered simultaneously. The nonlinear governing equations of motion of the axially moving viscoelastic belt for the in-plane and the out-of-plane are derived by the extended Hamilton's principle. The method of multiple scales and Galerkin's approach are applied directly to the partial differential governing equations of motion to obtain four-dimensional averaged equation under the case of one-to-one internal resonance and primary parametric resonance of the first order modes for the in-plane and the out-of-plane oscillations. Numerical method is used to investigate periodic and chaotic space motions of the axially moving viscoelastic belt. The results of numerical simulation demonstrate that there exist periodic, period-2, period-3, period-4, period-6, quasiperiodic and chaotic motions of the axially moving viscoelastic belt.