Transient response of a viscoelastic axially moving string with power constitutive model

In this paper, the transverse vibration of an initially stressed viscoelastic moving string is considered. The string material is assumed to obey the fractional differentiation constitutive law. The governing equation is obtained by Newtonian second law of motion and reduced to a set of nonlinear differential integral equations by using Galerkin's method. The differential integral equation system that contains fractional derivatives is then truncated to a finite dimensional one and solved numerically by using Runge-Kutta method and some other numerical manipulations. Finally, the numerical results are analyzed. The effects of elastic and viscoelastic parameters on the moving string and the variations of the nonlinear vibration with the changing of transport velocity and some other terms are investigated by numerical experiments.