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Two-dimensional rheological element in modelling of axially moving viscoelastic web
Institution:1. Institute for General Electrical Engineering, University of Rostock, Germany;2. Helmholtz-Zentrum Dresden–Rossendorf, Germany;1. Dipartimento di Fisica, Università di Torino, and INFN Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy;2. CERN Theory Unit, 1211 Geneva 23, Switzerland;3. Faculty of Education Science Technology and Mathematics, University of Canberra, Bruce ACT 2617, Australia;1. Department of Electrical Engineering and Computer Science, University of Liège, Sart Tilman B28, B-4000 Liège, Belgium;2. ORES, Louvain-la-Neuve, Belgium;1. Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland;2. LaBRI, CNRS and University of Bordeaux, 351, cours de la Libération, 33405 Talence cedex, France;3. GANG Project, Inria Paris and LIAFA, CNRS and Paris Diderot University, Case 7014, 75205 Paris Cedex 13, France
Abstract:To model the axially moving viscoelastic web material a two-dimensional rheological element is used in this paper. This model is formed by elastic region and viscoelastic region. Using two-dimensional rheological model and the plate theory the differential equation of motion in the form of the eighth-order linear partial differential equation that governs the transverse vibrations of the system is derived. The Galerkin method is applied to simplify the governing equation into two-order truncated system defined by the set of ordinary differential equations. Numerical investigations of dynamic stability of the paper web were carried out. The effects of the transport speed and the internal damping on the dynamic behaviour of the axially moving web are presented in this paper.
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