Transverse Nonlinear Vibrations of an Axially Accelerating Viscoelastic Belt

摘要

The non-planar transverse nonlinear vibrations of an axially accelerating viscoelastic belt with one-to-one internal resonance are investigated for the first time. The nonlinear equations of motion of an axially accelerating viscoelastic belt are developed using the generalized Hamilton's principle. The method of multiple scales and the 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 out-of-plane vibrations. Numerical method is used to investigate nonlinear dynamics characteristic of an axially accelerating viscoelastic belt. The results of numerical simulation show that there exist the periodic motion and the chaotic motion of an axially accelerating viscoelastic belt.