A stochastic dynamics approach for efficient incremental dynamic analysis

An approximate efficient stochastic incremental dynamic analysis (IDA) methodology based on stochastic averaging is developed for nonlinear oscillators. In this regard, an IDA surface is determined providing the probability density function (PDF) of the engineering demand parameter (EDP) for a given intensity measure (IM) value. In contrast to a computationally expensive Monte Carlo simulation (MCS) based determination of the IDA surface, the methodology developed herein determines the EDP PDF at minimal computational cost. The technique developed herein can account for physically realistic excitation models possessing not only time-varying intensities but time-varying frequency contents as well. A numerical example including a bilinear/hysteretic single-degree-of-freedom oscillator is analyzed, whereas comparisons with pertinent MCS data demonstrate the accuracy of the developed stochastic IDA methodology.