Frondelius T.

The aim of this study is to model the coupling between rotational vibrations of the rolls and longitudinal vibrations of an axially moving web. These vibrations are also known as changes in stress distribution. The web is treated as an axially moving rod. At the boundaries rolls are modelled such that the change in radius is taken into account, which makes it weakly non-linear. The mass flow out of the first roll and into the last one is correspondingly considered. In paper industry this is called unwinding and winding respectively. A magnetic tape, paper and aluminium webs are chosen for this study, because they are widely used and are therefore good and economically interesting materials to study for. The equation of motion and the boundary conditions are derived using the extended Hamilton's principle. The longitudinal frequencies of the axially moving bar is calculated numerically. Moreover, the forced vibrations of the time dependent model is solved by perturbation method and by time integration.