Drifting response of hysteretic oscillators to stochastic excitation

Under a zero-mean, broad-band, stationary-random load, the symmetric elastic perfectly plastic oscillator and many similar hysteretic systems exhibit a Brownian-like displacement response: asymptotically, the displacement mean vanishes and the displacement variance linearly increases with time. This diverging behavior, often referred to as the drift, is observed even when the excitation power spectrum vanishes at zero frequency, an instance so far lacking a satisfactory modeling within the framework of statistical linearization. The paper presents a linearization-based method which captures the drift in such an instance without requiring any simulation-calibrated parameter. The method combines statistical linearization with stochastic averaging and a generalized van der Pol transformation comprising terms introduced to make allowance for the drift. Model predictions are compared with Monte Carlo estimates for an excitation whose power spectrum vanishes at zero frequency. Good agreement is found for a wide range of excitation levels despite the extremeness of the non-linearity.