This paper deals with reducing transverse vibration for an axially moving string by a damped tensioner. The governing equation and the boundary conditions are derived for the system. Based on the analysis of the reflection and transmission of waves propagating along the string, the maximal energy dissipation is realized by determining the optimal damping. To simulate numerically the effect of vibration reduction, the Crank-Nicolson scheme is applied to discretize the governing equation of the string. The numerical results demonstrate the optimality of the determined damping in suppressing the transverse vibration.

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