Free Vibration Analysis of an Axially Travelling Web with Intermediate Elastic Supports

Abstract

The transverse vibration of axially travelling web may lead to poor quality of product in roll-to-roll manufacture, especially for the web with long span, which is usually installed with some elastic supports intermediately. This paper presents a mechanical model for predicting the dynamic behaviors of axially travelling web with intermediate elastic supports. Both of the axial movement and intermediate support are considered in this proposed model. The web is modeled as a thin plate and the elastic supports are modeled as monaxial springs. The derived equations of in-plane motion are linear and uncoupled with the transverse motion, whereas the equation of transverse motion is nonlinear and coupled with the in-plane motions. The Galerkin method is used to discretize the governing equations and compute natural frequencies. The numerical results agree well with the finite element results for the natural frequencies. The dynamic responses of the web are computed by employing the generalized-[Formula: see text] time integration method. A single intermediate elastic support case as well as multiple supports case are considered in this paper. The effects of the support position and stiffness on the natural frequency, stability and dynamic response of the travelling web are discussed.