Stochastic stability plays an important role in modern theories of nonlinear structural dynamics. Recently, more realistic models based on stochastic modelling and Itoˆ calculus, like flow induced vibrations and seismic excitations have been proposed. In this paper, the almost-sure asymptotic stability of some hamiltonian systems subjected to stochastic fluctuations is investigated. Dynamical systems are reduced to Itoˆ stochastic differential equations for the averaged hamiltonian by using a new stochastic averaging method. The stability of the original system is determined approximately by examining the behavior of the averaged hamiltonian. Analytical expressions for the stochastic stability exponents are obtained. The proposed procedure is illustrated on the Rayleigh Van der Pol Oscillator.

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