Nonlinear vibration of parametrically excited moving belts, part I: Dynamic response

The dynamic response and stability of parametrically excited viscoelastic belts are investigated in these two consecutive papers. In the first paper, the generalized equation of motion is obtained for a viscoelastic moving belt with geometric nonlinearity. The linear viscoelastic differential constitutive law is employed to characterize the material property of belts. The method of multiple scales is applied directly to the governing equation which is in the form of continuous gyroscopic systems. No assumptions regarding the spatial dependence of the motion are made. Closed-form solutions for the amplitude and the existence conditions of nontrivial limit cycles of the summation resonance are obtained. It is shown that there exists an upper boundary for the existence condition of the summation parametric resonance due to the existence of viscoelasticity. The effects of viscoelastic parameters, excitation frequencies, excitation amplitudes, and axial moving speeds on dynamic responses and existence boundaries are investigated.