Finite difference method for simulating transverse vibrations of an axially moving viscoelastic string

A finite difference method is presented to simulate transverse vibrations of an axially moving string. By discretizing the governing equation and the equation of stress-strain relation at different frictional knots, two linear sparse finite difference equation systems are obtained. The two explicit difference schemes can be calculated alternatively, which make the computation much more efficient. The numerical method makes the nonlinear model easier to deal with and of truncation errors, O(Δt² + Δx²). It also shows quite good stability for small initial values. Numerical examples are presented to demonstrate the efficiency and the stability of the algorithm, and dynamic analysis of a viscoelastic string is given by using the numerical results.