The nonlinear dynamic analysis is performed on parametrically excited, viscoelastic moving-belts at summation resonance. The belt material behavior is described by a Voigt-Kelvin model. Closed-form solutions are derived at the first order approximation. Focus is put on the stability of the nontrivial solutions. The explicit expressions on the stability conditions are obtained, and then simplified through numerical simulations. The influences of moving speed and tension fluctuation on the stability of the nontrivial solutions are also demonstrated.
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