International Applied Mechanics

, Volume 46, Issue 4, pp 474–490 | Cite as

Stochastic stability of three-dimensional linear systems under parametric random action

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The stability of a three-dimensional linear system, driven by a parametric random excitation is considered. The stability of the system is investigated using a combination of stochastic averaging method and a probabilistic approach. For this purpose, it is necessary to find the transient probability density of the components of the vector random process. Thus, the invariant measure of the system may be calculated from the stationary solutions of the associated Fokker–Planck equations. These solutions are obtained numerically, using the sweep method. As a comparison criterion, a digital simulation of Itô equations has been carried out using the Monte-Carlo simulation (MCS) method. As an application, the example of instability of a thin-walled bar under the effect of parametric random action is considered

Keywords

stochastic stability stochastic averaging method transient probability density Monte-Carlo simulation method sweep method 
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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.University of Hawaii at ManoaHonoluluUSA

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