Recursive Modeling of Dynamic Systems

Abstract

The dynamic response analysis of structural systems to a variety of random excitations using recursive models is presented. The methodology permits analysis of stationary, nonstationary, or transient response of structures under stochastic loads, e.g., correlated multi‐input loading due to fluctuations in wind or wave surface profile, or seismic excitation. For the nonstationary, or transient, excitation, the analysis involves a direct computation of the output covariance from a given nonstationary correlation structure of the input. The accuracy and stability of the simulated time histories is assessed. A detailed example is presented to illustrate the proposed recursive model. The concept of an ARMA (auto‐regressive moving average) system is presented in which the ARMA representation of the response is obtained in terms of the ARMA description of the stationary excitation. The usefulness of the recursive approach for nonlinear systems is demonstrated by means of an example involving an elasto‐plastic beam subjected to a suddenly applied load.