0
Research Papers

Aeroelastic Stability of Wide Webs and Narrow Ribbons in Cross Flow

[+] Author and Article Information
Rahul A. Bidkar, Anil K. Bajaj

Dynamic Systems and Stability Laboratory, School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907

Arvind Raman

Dynamic Systems and Stability Laboratory, School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907raman@ecn.purdue.edu

See Sec. 6 for a discussion on the validity of this assumption.

For higher basis functions, a fluid particle traveling tangentially to the web surface turns through smaller radii of curvature, giving rise to larger centrifugal pressures, which in turn leads to a more rapid fluid-induced reduction in stiffness compared to the lower basis functions.

Based on the large Reynolds number and the small web oscillation amplitude, the use of the unsteady Kutta condition is valid (18,25) even at such high reduced frequencies k=(ωb)(2V) ranging from 0 to 15.

See the Appendix for the definition of the various matrices.

J. Appl. Mech 75(4), 041023 (May 19, 2008) (9 pages) doi:10.1115/1.2871192 History: Received June 26, 2007; Revised October 30, 2007; Published May 19, 2008

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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2008 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 2

A schematic representation showing the arrangement of panels and vortex rings on the half-web and in the wake

Grahic Jump Location
Figure 3

Behavior of the perturbation aerodynamic potential along the X and Y axes

Grahic Jump Location
Figure 4

The first mode shape at zero cross flow velocity for (a) in vacuo web, (b) web with surrounding air, and (c) relative contributions of the structural basis functions to the first mode of the fluid-web system

Grahic Jump Location
Figure 1

A Schematic for the uniaxially tensioned stationary web subjected to cross flow

Grahic Jump Location
Figure 5

The envelope and the phase of the first mode of the coupled fluid-web system along with the relative contributions of the structural basis functions at (a) V=0.035, (b) V=0.045, and (c) V=0.055

Grahic Jump Location
Figure 6

Nondimensional frequencies and rates of growth of the first five modes of a fluid-web system of aspect ratio κ=1 and tension ratio ϵ=5×10−6

Grahic Jump Location
Figure 7

Stability regions in the V-ϵ plane for a fluid-web system of aspect ratio κ=1

Grahic Jump Location
Figure 8

Nondimensional frequencies and rates of growth for a ribbon of aspect ratio κ=30 with (a) ϵ=5×10−6 and (b) ϵ=5.5×10−9

Grahic Jump Location
Figure 9

Mode shapes of a narrow ribbon of κ=30: (a) first mode at V=0.03 and ϵ=5×10−6, (b) second mode at V=0.03 and ϵ=5×10−6, and (c) fourth mode at V=0.0139 and ϵ=5.5×10−9

Grahic Jump Location
Figure 10

Stability regions in the V-ϵ plane for a narrow ribbon of aspect ratio κ=30

Grahic Jump Location
Figure 11

Comparison of the frequencies of a narrow ribbon (κ=30), a wide ribbon (κ=5), and a wide web (κ=1)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In