Nonlinear dynamic behavior of a moving viscoelastic string undergoing three-dimensional vibration

This paper is devoted to the investigation of bifurcation and chaos of a moving viscoelastic string undergoing three-dimensional vibration. An initially stressed viscoelastic string subjected to constant axial motion and harmonical tension is considered. The string material is assumed to be constituted by spring-dashpot model which is considered as the Voigt element in series with a spring (three-parameter model). Using constitutive law of differential type method we can obtain the partial differential equations of motion. Then the partial differential equations can be approximated by means of Galerkin’s method. The axial–lateral coupled effect of the viscoelastic string is digged out by comparing the numerical results of the three-dimensional vibration analysis and the only transverse vibration analysis. The responses of the viscoelastic string and the elastic string are compared. Using the FFT spectra, Poincare maps, and the bifurcation diagrams, the responses of the viscoelastic string are classified. The effects of the material parameters, the wave propagation speed ratio, the transport speed and the frequency of axially tension on the response amplitudes are investigated.