An approximate approach for assessing the reliability of a stochastically excited softening Duffing oscillator Zhang, Yuanjin; Kougioumtzoglou, Ioannis A.
An approximate analytical technique for assessing the reliability of a softening Duffing oscillator subject to evolutionary stochastic excitation is developed. Specifically, relying on a stochastic averaging treatment of the problem the oscillator time-varying survival probability is determined in a computationally efficient manner. In comparison with previous techniques that neglect the potential unbounded response behavior of the oscillator when the restoring force acquires negative values, the herein developed technique readily takes this aspect into account by introducing a special form for the oscillator non-stationary response amplitude probability density function (PDF). A significant advantage of the technique relates to the fact that it can readily handle cases of stochastic excitations that exhibit strong variability in both the intensity and the frequency content. An illustrative numerical example of a softening Duffing oscillator subject to earthquake excitation is included. Comparisons with pertinent Monte Carlo simulation data demonstrate the efficiency of the technique.
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