Non-linear free oscillations of moving viscoelastic belts

In order to investigate more precisely the effect of material damping on the non-linear free vibration of moving belts, the standard linear solid model containing three elements is used to represent the belt material property. By reforming the equations for motion of the system concerned and directly applying the method of multiple scales, a new approach is suggested, which yields closed form solutions in the first order approximation to free vibration response. The solutions are furthermore degenerated to the solutions of an elastic model and two viscoelastic models, a Kelvin model and a Maxwell model. Simplified solutions of both the standard model and Maxwell model are obtained under certain conditions. Both the degeneration and simplification reveal the relation and difference among different models. Numerical simulations are carried out on using the standard linear solid to show the influence of different design parameters on the non-linear vibration frequency and amplitude. Preliminary comparisons are also made to evaluate the accuracy of the simplified solutions and to show the discrepancy of using elastic model, the standard linear solid, the Kelvin model and the Maxwell model.