Chinese Journal of Theoretical and Applied Mechani ›› 2008, Vol. 40 ›› Issue (3): 421-432.DOI: 10.6052/0459-1879-2008-3-2006-626

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Transverse nonlinear nonplanar dynamics of an axially moving viscoelastic belt with integral constitutive law

Yanqi Liu Wei Zhang Meijuan Gao Xiaoli Yang   

  1. College of Mechanical Engineering, Beijing University of Technology, Beijing 100022, China College of Mechanical Engineering, Beijing University of Technology, Beijing 100022, China College of Mechanical Engineering, Beijing University of Technology, Beijing 100022, China College of Mechanical Engineering, Beijing University of Technology, Beijing 100022, China
  • Received:2006-12-18 Revised:2007-09-19 Online:2008-05-25 Published:1900-01-01

Abstract: In this paper, the problem of the transverse nonlinear nonplanar oscillations of an axially moving viscoelastic belt with the integral constitutive law are investigated in the case of 1:1 internal resonance. The governing equations of this problem are firstly derived with the generalized Hamilton's principle to obtain the in-plane and out-of-plane transverse nonlinear oscillations of the axially moving viscoelastic belt neglecting the axially deformation. Perturbation analyses are carried out on these partial differential governing equations with the multiscale method and the Galerkin's approach to obtain four-dimensional averaged equations and to analyze the stabilities of the solution in the dynamic system. The simulation results show the periodic motion, the quasi-periodic motion and the chaotic motion in the transverse nonlinear nonplanar oscillations of the axially moving viscoelastic belt.

Key words: viscoelastic belt, nonlinear, transverse vibration, internal resonance, chaos