A numerical algorithm for non-linear parametric vibration analysis of a viscoelastic moving belt

A numerical algorithm for nonlinear partial differential equations is proposed to analyze the parametric vibrations of viscoelastic moving belts. The method of finite difference is employed to discrete spatial variables. The partial differential equation is transformed into a large system of differential-algebraic equations. Based oil the special structures in the mathematical model of a viscoelastic belt, the algorithm is easy to carry out, and it can be efficiently applied to solve the parametric vibration problems of belts with various kinds of nonlinear stress-strain relations. As two applications of the algorithm, the dynamical response of viscoelastic belts, whose materials are respectively defined by the standard model or the Maxwell-Kelvin model, are calculated.