The nonlinear forced vibration 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 nonlinearities by adopting the linear viscoelastic differential constitutive law. The method of multiple scales is applied directly to the governing partial differential 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. Effects of elastic and viscoelastic parameters, axial moving speed, and the geometric nonlinearity on the system response are also studied.
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