Modeling of damage accumulation for Duffing-type systems under severe random excitations

The focus of this investigation is on the prediction of the fatigue life of aircraft panels subjected to thermal effects and a severe random acoustic excitation. The prototypical equations for this problem, i.e. the single and double well Duffing oscillators subjected to a bandlimited white noise, are first considered. A review of some currently available approaches, i.e. the Rayleigh approximation and the single spectral moment method both with and without Gaussianity correction, strongly suggests that an accurate prediction of the fatigue life for this non-linear system requires a dedicated model. To this end, an approximation of the probability density function of the peaks of the stationary response of the Duffing oscillators is derived. This model is then used in conjunction with either a narrowband assumption or the single spectral moment methodology to yield a prediction of the fatigue life. The application of this approach to simulation data from both single and double well Duffing oscillators, as well as on the experimental response of an unbuckled panel, demonstrates the reliability of this novel approximation.