Nonlinear dynamical analysis of axially moving viscoelastic strings

In this paper, nonlinear dynamical behaviors of axially moving viscoelastic strings are investigated. The one-term and the two-term Galerkin truncations using translating string eigenfunctions are respectively employed to reduce the partial-differential equation that governs the transverse motions of the string to a set of ordinary differential equations. The bifurcation diagrams are presented in the case that the amplitude of the periodic perturbation, or the dynamic viscosity is respectively varied while other parameters are fixed. The dynamical behaviors are numerically identified based on the Poincare maps. Numerical results show that regular and chaotic motions occur in the transverse vibration of the axially moving viscoelastic strings.