Observations on the vibrations of paper webs

Abstract

Frequency clustering and edge vibration localization of thin, wide, high-speed translating webs are investigated using a linear, translating, tensioned Kirchhoff plate model with very small but finite bending stiffness to tension ratio. Non-uniform tensioning, and vibration coupling of the web with a incompressible potential flow are included in the model. Such webs are commonly found in paper, plastic, polymer sheet and metal foil processing, in gravure and offset web printing machines, and in magnetic and optical tapes. The presence of frequency clusters, its impact on free edge vibration localization, and its dependence on transport speed, and non-uniformity of tension are analyzed using a Galerkin discretization of the equations of motion. Experiments are performed on an acoustically excited, stationary, taut paper web. The experimental results demonstrate clearly the presence of frequency clustering and its dynamic effects. The results are expected to have significant implications for the further studies on the modal analysis and nonlinear mechanics of high-speed web systems.