On Travelling Web Stability Including Material Viscoelasticity and Surrounding Air

Abstract

The aim of this research is to gain more understanding of the physics of the transportation of materials having viscoelastic characteristics, high transport speeds, a small thickness and a large surface area. This study introduces new models that take into account both material viscoelasticity and the fluid-structure interaction between the travel- ling material and the surrounding owing fluid. A web (continuum) travelling between two fixed supports is considered, modelling the web as a Kelvin–Voigt type viscoelastic panel and the air ow as a potential ow. Stability of the system is studied with the help of its eigenfrequencies (eigenvalues) for two different types of ow geometries. First, a ow inside an enclosure with a rectangular cross-direction, through which the panel is travelling, is added to the equations of out-of-plane motion of the panel with the help of added mass coefficients. Secondly, a free stream potential ow obstructed by the travelling panel is analyzed using the analytical solution for the aerodynamic reaction pressure. Some numerical examples are given for both models.