A stochastic dynamics approach for response spectrum analysis of bilinear systems using time-dependent equivalent linear properties Giaralis, Agathoklis; Kougioumtzoglou, Ioannis A.
A stochastic averaging approach is used in conjunction with non-stationary response spectrum compatible random processes to derive time-varying effective linear properties (ELPs), namely damping ratio and natural frequency, for bilinear hysteretic oscillators subject to seismic excitation specified by an elastic response spectrum. It is shown numerically that the peak response of linear oscillators defined by these ELPs at the time instant for which the variance of either the excitation process or the estimated non-linear response process approximates well the peak inelastic response of a given bilinear oscillator. This is demonstrated by considering a uniformly modulated random process compatible with the Eurocode 8 (EC8) elastic response spectrum to derive ELPs from bilinear oscillators of various properties, and an ensemble of 40 artificial EC8 compatible non-stationary accelerograms to obtain peak responses of the same oscillators in a Monte Carlo based analysis. The reported numerical data suggest that peak response of bilinear hysteretic systems can be reliably estimated by the peak response of surrogate linear systems without the need to undertake nonlinear response history analysis for seismic excitation represented by appropriate non-stationary random processes.
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