Non-linear vibrations of viscoelastic moving belts, part I: Free vibration analysis

The non-linear free vibration of viscoelastic moving belts is studied. Based on the linear viscoelastic differential constitutive law, the generalized equation of motion is derived for a moving belt with geometric non-linearities. The method of multiple scales is applied directly to the governing equation which is in the form of continuous autonomous gyroscopic systems with weak non-linearity. This direct treatment does not involve a prior assumption regarding the spatial solutions. The non-linear natural frequencies and free response amplitude for autonomous systems are predicted by the perturbation method. The results obtained with the quasi-static assumption and those without this assumption are compared. The effects of elastic and viscoelastic parameters, axial moving speed, and the geometric non-linearity on natural frequencies and amplitudes of the free response are investigated from numerical examples.