An approximate Markov process for a function of the system response of a class of lightly damped, nonlinear random vibration problems is derived using the method of stochastic averaging. The solution of the associated forward Kolmogorov equation for the transition probability density function is presented. The merit of this solution is demonstrated by deriving the spectral density of the system stationary response to step‐modulated white noise. The reliability of the results is assessed by performing appropriate Monte Carlo simulations.
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Spanos et al. (1988) studied this question.
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