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Transient Growth Before Coupled-Mode Flutter

[+] Author Affiliations
Peter Schmid, Emmanuel de Langre

École Polytechnique, Palaiseau, France

Paper No. IMECE2002-32200, pp. 1055-1064; 10 pages
doi:10.1115/IMECE2002-32200
From:
  • ASME 2002 International Mechanical Engineering Congress and Exposition
  • 5th International Symposium on Fluid Structure Interaction, Aeroelasticity, and Flow Induced Vibration and Noise
  • New Orleans, Louisiana, USA, November 17–22, 2002
  • Conference Sponsors: Applied Mechanics Division
  • ISBN: 0-7918-3659-2 | eISBN: 0-7918-1691-5, 0-7918-1692-3, 0-7918-1693-1
  • Copyright © 2002 by ASME

abstract

Transient growth of energy is known to occur even in stable dynamical systems due to the non-normality of the underlying linear operator. This has been the object of growing attention in the field of hydrodynamic stability, where linearly stable flows may be found to be strongly nonlinearly unstable as a consequence of transient growth. We apply these concepts to the generic case of coupled-mode flutter, which is a mechanism with important applications in the field of fluid-structure interactions. Using numerical and analytical approaches on a simple system with two degrees of freedom and anti-symmetric coupling we show that the energy of such a system may grow by a factor of more than 10, before the threshold of coupled-mode flutter is crossed. This growth is a simple consequence of the non-orthogonality of modes arising from the non-conservative forces. These general results are then applied to three cases in the field of flow-induced vibrations: (a) panel flutter (two-degrees-of-freedom model, as used by Dowell (1995)), (b) follower force (two-degrees-of-freedom model as used by Bamberger (1981)), and (c) fluid-conveying pipes (two-degree-of-freedom model, as used by Benjamin (1961) and Paidoussis (1998)), for different mass ratios. For these three cases we show that the magnitude of transient growth of mechanical energy before the onset of coupled-mode flutter is substantial enough to cause a significant discrepancy between the apparent threshold of instability and the one predicted by linear stability theory.

Copyright © 2002 by ASME

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