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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Dynamics of randomly perturbed nonlinear gyroscopic systems
The objective of this work is to study the long term effects of small
dissipative, symmetry-breaking and noisy perturbations on the dynamics of
a two-degree-of-freedom nonlinear gyroscopic system. The results
derived here are applied to study the dynamics of a rotating shaft subjected to
stochastic loading, but these results can be applied to any general gyroscopic
system. A stochastic averaging method is developed to reduce the
dimension of the original four dimensional system. This provides a qualitatively
accurate and computationally feasible description of the system.
Making use of the interaction between the gyroscopic and dissipative forces,
the original problem is reduced to a one dimensional diffusive Markov process.
Depending on the system parameters, the reduced Markov process takes its
values on a line or a graph. Finally, the Fokker Planck Equation(FPE) is
solved to obtain the stationary probability density function.}
Lalit Vedula and N. Sri Namachchivaya, ``Stochastically perturbed nonlinear gyroscopic
systems: Application to rotating shafts", Probabilistic Mechanics Conference,
July 24-26, Notre Dame, IN.
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