Incremental Dynamic Analysis: A Nonlinear Stochastic Dynamics Perspective

Abstract

AbstractAn 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 surf...