Director:
N. Sri. Namachchivaya
306 Talbot Laboratory,
104 South Wright Street
Urbana, IL 61801
Phone: (217) 244-0683,
Fax: (217) 244-0720
E-mail: navam@uiuc.edu
Department of
Aerospace Engineering
Created: 11/16/2003
Last Updated: 11/16/2003
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Stabilization of linear
systems by real noise
In a recent paper, Popp and Romberg~\cite{Pop99} reported on stabilization
by grid generated turbulence of a smooth circular cylinder immersed in the
wake from an identical cylinder in an array of aluminum tubes.
Although these results were obtained experimentally, so far they have
not been explained from a stochastic point of view on a rigorous theoretical basis.
This paper provides analytical results which may explain this stabilization
phenomenon by modeling the immersed cylinder as a two-degree of freedom
oscillator and the turbulence as a stochastic process.
We obtain general asymptotic approximation for the moment Lyapunov exponent,
$g(p)$, and the Lyapunov exponent, $\lambda$, for a four dimensional
system with one critical mode and another asymptotically stable
mode driven by a small intensity stochastic process.
These results, pertaining to $p^{th}$ moment stability and almost-sure
stability, explain how the stochastic components which couple
the stable and the critical modes play an important role in
determining whether a noisy excitation can stabilize or destabilize
the oscillatory critical mode. They are then applied to a prototypical
flow induced oscillation model to explain the experimental
results.
N. Sri Namachchivaya and Lalit Vedula, "Stabilization of linear
systems by real noise: Application to flow induced oscillations",
Journal of Dynamics and Stability of Systems, Vol. 15(2), 2000, pp. 185-208.
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