Numerical damping of oscillations of a moving string

Abstract

The basis of this research is the mechanical processes that take place in the production of paper. All papermaking machines contain open sections of the web between the support rollers. When the paper web moves, it may lose stability, break, or begin to make transverse vibrations. It is assumed that the amplitude of these vibrations is the same in the width direction of the web, so that the movement of the string in the axial direction with constant speed is considered as a model. It should be noted that because of the axial motion, the mechanics of moving materials are different from classical mechanics. In the paper, the decrease of vibrations is realized with the help of actuators. The motion of the string is modelled by the initial-boundary value problem for a partial differential equation of hyperbolic type. The vibration damping controlling actuators are modelled by the function on the right side of this equation. The problem is to damp the forced transverse vibrations of a moving string in a minimum time. Examples of calculations are given.