Drifting response of elastic perfectly plastic oscillators under zero mean random load

The displacement response of an elastic perfectly plastic oscillator under a zero mean, stationary, broad band random load is known not to reach stationarity: asymptotically, its mean is zero but its variance linearly increases with time. Thus, as time passes the oscillator gradually drifts away from its initial position. A method is presented for estimating the time asymptotic behavior of this drifting. Developed within the context of stochastic averaging, the method is based on a generalized van der Pol transformation that differs from its classical counterpart by an extra term that is meant to capture the drifting. The introduction of this term makes it possible to successfully address the drifting by using a linearization technique, even when the excitation power spectrum vanishes at zero frequency. The results obtained with the method are in good agreement with Monte Carlo simulation estimates.