Aeroelastic Stability of Wide Webs and Narrow Ribbons in Cross Flow

Abstract

Aeroelastic flutter can lead to large amplitude oscillations of tensioned wide webs and narrow ribbons commonly used in the paper-handling, textile, sheet-metal, and plastics industries. In this article, we examine the aeroelastic stability of a web or a ribbon, which is submerged in an incompressible and inviscid fluid flow across its free edges. The web or ribbon is modeled as a uniaxially tensioned Kirchhoff plate with vanishingly small bending stiffness. A Galerkin discretization for the structural dynamics together with panel methods for the unsteady three dimensional potential flow are used to cast the coupled system into the form of a gyroscopic, nonconservative dynamical system. It is found that wide webs mainly destabilize through a divergence instability due to the cross-flow-induced conservative centrifugal effects. However, for certain values of applied tension, the wake-induced nonconservative effects can destabilize the web via a weak flutter instability. Contrarily, narrow ribbons in cross flow are nearly equally likely to undergo flutter or divergence instability depending on the value of applied tension.