An analytic explanation is given for the experimental results reported by Popp and Romberg (2001, “Influence of Stochastic Effects on Flow Induced Vibrations in Tube Bundles,” IUTAM Symposium on Nonlinearity and Stochastic Structural Dynamics (Solid Mechanics and Its Applications), S. Narayanan and R. N. Iyengar, eds., Kluwer Academic, Dordrecht, Vol. 85, pp. 197–208) on fluid flow over tube bundles by using the concept of the maximal Lyapunov exponent. The motion of one tube in the bundle is modeled as a two-degree-of-freedom (four dimensional) system with one critical mode and one asymptotically stable mode driven by a small intensity stochastic process. We obtain a general asymptotic approximation for the maximal Lyapunov exponent for this four dimensional system and explain how the stochastic components that couple the critical and stable modes play an important role in determining whether a noisy excitation can stabilize or destabilize the oscillatory critical mode.
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Research Papers
Stochastic Stability of Coupled Oscillators With One Asymptotically Stable and One Critical Mode
N. Sri Namachchivaya,
N. Sri Namachchivaya
Department of Aerospace Engineering,
e-mail: navam@illinois.edu
University of Illinois
, Urbana, IL 61801-2958
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Lalit Vedula,
Lalit Vedula
Department of Aerospace Engineering,
University of Illinois
, Urbana, IL 61801-2958
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Kristjan Onu
Kristjan Onu
Department of Aerospace Engineering,
University of Illinois
, Urbana, IL 61801-2958
Search for other works by this author on:
N. Sri Namachchivaya
Department of Aerospace Engineering,
University of Illinois
, Urbana, IL 61801-2958e-mail: navam@illinois.edu
Lalit Vedula
Department of Aerospace Engineering,
University of Illinois
, Urbana, IL 61801-2958
Kristjan Onu
Department of Aerospace Engineering,
University of Illinois
, Urbana, IL 61801-2958J. Appl. Mech. May 2011, 78(3): 031013 (9 pages)
Published Online: February 15, 2011
Article history
Received:
December 15, 2009
Revised:
December 24, 2010
Posted:
January 5, 2011
Published:
February 15, 2011
Online:
February 15, 2011
Citation
Sri Namachchivaya, N., Vedula, L., and Onu, K. (February 15, 2011). "Stochastic Stability of Coupled Oscillators With One Asymptotically Stable and One Critical Mode." ASME. J. Appl. Mech. May 2011; 78(3): 031013. https://doi.org/10.1115/1.4003362
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