Softening Duffing Oscillator Reliability Assessment Subject to Evolutionary Stochastic Excitation

Abstract

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-dependent 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 stiffness element acquires negative values, the technique developed in this paper readily takes this aspect into account by introducing a special form for the oscillator nonstationary 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 variability in both the intensity and the frequency content. Numerical examples include a softening Duffing oscillator under evolutionary earthquake excitation and a softening Duffing oscillator with nonlinear damping modeling the nonlinear ship roll motion in beam seas. Comparisons with pertinent Monte Carlo simulation data demonstrate the efficiency of the technique.