Transverse vibration and instability of axially travelling web subjected to non-homogeneous tension

Abstract

In many engineering applications of roll-to-roll manufacturing, the inhomogeneity in the tension profile applied at both the ends of web is apparent, which cannot be completely ignored in the modeling so as to accurately predict the dynamic behaviors of the travelling web. In this paper, transverse vibration and instability of axially travelling web subjected to parabolic tension profile are investigated. The governing equations of motion are derived by employing the Hamilton principle. The Galerkin method is used to compute the complex natural frequencies and mode shapes. The instability of travelling web versus different axial velocities is studied. This paper focuses on the influence of tension inhomogeneity on the critical velocity and mode shape. The sensitivity of aspect ratio and average tension to the tension inhomogeneity are also discussed. The critical velocities of the travelling web may be greatly decreased because of the tension inhomogeneity and a small tension inhomogeneity is enough to change the mode shapes completely.