Transverse vibration control of translating visco-elastically connected double-string-like continua

The aim of this work is to develop a direct and exact approach using the Green's functions to control the steady-state transverse vibration of an axially moving double-string system supported by two rollers (eyelets) at both ends. The two strings are similar and coupled by a viscoelastic layer of a Kelvin–Voigt type. The control is achieved by introducing suitable control forces (using actuators) or passive elements to be located at some chosen locations along the span between the eyelets. A scheme is proposed for evaluating the control forces and their locations to suppress the vibration of the system and correspondingly decrease the generated noise. The variation of the running speed and different end supports are taken into consideration.