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Research Papers

Stochastic Stability of Coupled Oscillators With One Asymptotically Stable and One Critical Mode

[+] Author and Article Information
N. Sri Namachchivaya1

Department of Aerospace Engineering, University of Illinois, Urbana, IL 61801-2958navam@illinois.edu

Lalit Vedula

Department of Aerospace Engineering, University of Illinois, Urbana, IL 61801-2958

Kristjan Onu2

Department of Aerospace Engineering, University of Illinois, Urbana, IL 61801-2958

1

Corresponding author.

2

Also at Department of Mechanical Science and Engineering.

J. Appl. Mech 78(3), 031013 (Feb 15, 2011) (9 pages) doi:10.1115/1.4003362 History: Received December 15, 2009; Revised December 24, 2010; Posted January 05, 2011; Published February 15, 2011; Online February 15, 2011

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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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Illustration of the mechanical system

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Figure 2

Shifting of the stability boundary due to the introduction of real noise

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Figure 3

Variation in λ with the filter parameters β and S0(Vcr=23.5 m/s)

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