6533b829fe1ef96bd128a1d9

RESEARCH PRODUCT

Travelling Panels Made of Viscoelastic Material

subject

description

In this chapter, our focus is to analyse the behaviour of moving panels using viscoelastic materials. As the reader will have noticed, all the models discussed in previous chapters have concerned the case of a purely elastic material. The deformation of an elastic material depends only on the applied forces; it has no explicit time dependence. Paper, however, is a more complicated material: it is viscoelastic. In addition to elastic properties, it has also time-dependent viscous properties, which cause the phenomena of creep and relaxation (see, e.g., Alava and Niskanen 2006). One of the simplest models for a viscoelastic solid is the Kelvin–Voigt model, which consists of a linear spring and a dashpot (damper) connected in parallel. In this chapter, we will use dynamic (modal) analysis to investigate the stability of an axially moving viscoelastic Kelvin–Voigt panel. The material derivative will be used in the viscoelastic constitutive relations. A similar analysis has been performed in the papers by Marynowski and Kapitaniak (2002) and Lee and Oh (2005), but using the partial time derivative in the viscoelastic constitutive relations. We will present comparisons of the results using the material derivative with the results obtained using the partial time derivative.