Non-linear vibrations of viscoelastic moving belts, part II: Forced vibration analysis

The non-linear forced fibration of viscoelastic moving belts excited by the eccentricity of pulleys is investigated. The generalized equations of motion are derived for a viscoelastic moving belt with geometric non-linearities by adopting the linear viscoelastic differential constitutive law. The method of multiple scales is applied directly to the governing equations which are in the form of continuous non-autonomous gyroscopic systems. The amplitude of near- and exact-resonant steady state response for non-autonomous systems is predicted. The results obtained with quasi-static assumption and those without this assumption are compared. Effects of elastic and viscoelastic parameters, axial moving speed, and the geometric non-linearity on the system response are also studied.