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

摘要

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.