Incremental Dynamic Analysis: A Nonlinear Stochastic Dynamics Perspective

Ketson R.M. dos Santos

doi:10.1061/(ASCE)EM.1943-7889.0001129

2016-10-01

PRE

Ketson R.M. dos Santos

Ioannis A. Kougioumtzoglou *

André T. Beck

DOI：10.1061/(ASCE)EM.1943-7889.0001129

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摘要

En 中文

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. (C) 2016 American Society of Civil Engineers.

Keyword:

Incremental dynamic analysis

Stochastic process

Stochastic dynamics

Nonlinear system

Stochastic averaging

Statistical linearization

Performance-based engineering