In this paper, the stochastic stability of the three elastically connected Euler beams on elastic foundation is studied. The model is given as three coupled oscillators. Stochastic stability conditions are expressed by the Lyapunov exponent and moment Lyapunov exponents. It is determined that the new set of transformation for getting differential equations can be applied for any system of three coupled oscillators. The method of regular perturbation is used to determine the asymptotic expressions for these exponents in the presence of small intensity noises. Analytical results are presented for the almost sure and moment stability of a stochastic dynamical system. The results are applied to study the moment stability of the complex structure with influence of the white noise excitation due to the axial compressive stochastic load.
Moment Lyapunov Exponents and Stochastic Stability of a Three-Dimensional System on Elastic Foundation Using a Perturbation Approach
University of Niš,
Manuscript received May 6, 2012; final manuscript received December 29, 2012; accepted manuscript posted January 29, 2013; published online July 12, 2013. Assoc. Editor: Wei-Chau Xie.
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Stojanović, V., and Petković, M. (July 12, 2013). "Moment Lyapunov Exponents and Stochastic Stability of a Three-Dimensional System on Elastic Foundation Using a Perturbation Approach." ASME. J. Appl. Mech. September 2013; 80(5): 051009. https://doi.org/10.1115/1.4023519
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