Incremental dynamic analysis: A nonlinear stochastic dynamics perspective

An efficient stochastic incremental dynamic analysis (IDA) methodology for nonlinear/hysteretic oscillators is developed by resorting to nonlinear stochastic dynamics concepts and tools such as stochastic averaging and statistical linearization. Specifically, modeling the excitation as a nonstationary stochastic process possessing an evolutionary power spectrum (EPS), an approximate closed-form expression is derived for the parameterized oscillator response amplitude probability density function (PDF). In this regard, an IDA surface is determined providing the 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. Further, an approximate closed-form expression is derived for the parameterized nonlinear oscillator response EPS as well; thus, a conceptually novel IDA surface is determined where the EDP relates to the nonlinear oscillator response EPS. The stochastic IDA framework can account for physically realistic excitation models possessing not only time-varying intensities but time-varying frequency contents as well. A bilinear/hysteretic single-degree-of-freedom oscillator is considered as a numerical example, whereas comparisons with pertinent MCS data demonstrate the accuracy and efficiency of the developed stochastic IDA methodology.