A numerical method for simulating transverse vibrations of an axially moving string

A modified finite difference method is presented to simulate transverse vibrations of an axially moving string. By discretizing the governing equation and the stress-strain relation at different frictional knots, two linear sparse finite difference equations are obtained, which can be computed alternatively. The numerical method makes the non-linear model easier to deal with and of small truncation errors. It also shows stable for small initial values, so it can be used in analyzing the non-linear vibration of viscoelastic moving string efficiently. A practical way of testing the precise of the numerical results is given by using a conservative quantity. Numerical examples are presented and dynamical analysis is given by using the numerical results.