Longitudinal Vibrations of the Viscoelastic Moving Belt

The longitudinal dynamic governing equation of the viscoelastic belt with one end subjected to concentrated mass was established based on the Kelvin-Voigt viscoelastic partial-differential constitutive law. The generalized coordinate method was adopted to solve dynamic displacement and dynamic tension. And then it was reduced to be a nonhomogeneous partial-differential equation where the analytical solutions with a constant acceleration were obtained. The effects of damping coefficient, the loading radio, and the constant acceleration of the belt on the dynamic response of the belt were investigated using the established dynamic model. The results show that the longitudinal vibration frequency of the viscoelastic moving belt increases with an increasing of the mass at the end. The increasing value of the loading radio, damping coefficient, and decreasing the acceleration will lead to a deceasing in dynamic tension. Moreover, the method of solution can be applied to axially moving viscoelastic materials with different boundary conditions.