Estimation of time to stationarity in geometrically nonlinear structural responses

The determination of the time to stationarity is defined here through the convergence, to its stationary limit, of the nonstationary variance. This function is estimated through Monte Carlo simulations and a two-step, autoregressive-based modeling approach is employed to minimize the effects of randomness introduced by the limited number of simulations that can be carried out. The methodology is applied extensively to nonlinear single-degree-of-freedom models but is also demonstrated on 8-mode reduced order models of clamped–clamped straight and curved beams. In the latter case, it is found that the time to stationarity is strongly dependent on the excitation level, i.e. varying from one case to another by a factor at least larger than 4, thereby emphasizing the interest in estimating it beforehand. It is finally shown that the single-degree-of-freedom results tabulated here may be used for these reduced order models to obtain a first estimate of the time to stationarity.