On Galerkin Discretization of Axially Moving Nonlinear Strings

A computational technique is proposed for the Galerkin discretization of axially moving strings with geometric nonlinearity. The Galerkin discretization is based on the eigenfunctions of stationary strings. The discretized equations are simplified by regrouping nonlinear terms to reduce the computation work. The scheme can be easily implemented in the practical programming. Numerical results show the effectiveness of the technique. The results also highlight the feature of Galerkin's discretization of gyroscopic continua that the term number in Galerkin's discretization should be even. The technique is generalized from elastic strings to viscoelastic strings.