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-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. Numerical examples include a softening Duffing oscillator under evolutionary earthquake excitation, as well as 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.

On the Effect of the Electrical Load on Vibration Energy Harvesting Under Stochastic Resonance

“…The joint PDF of nonlinear oscillators is particularly difficult to obtain analytically apart from certain exceptions. To overcome this, computational and approximate analytical methods are used to study in detail the stochastic dynamics of nonlinear oscillators ( [8], [13]- [14]). Crosswell oscillations of bi-stable energy harvesters have also been proposed for combined harmonic and stochastic excitation [15].…”