A Stochastic Dynamics Approach for Response Determination of Bilinear Hysteretic Systems To Pulse-Like Ground Motions Using Time-Dependent Equivalent Linear Properties

Abstract eng:
A non-stationary stochastic averaging/linearization formulation is considered in conjunction with a phenomenological stochastic model for pulse-like ground motions (PLGMs) to probe into the response of bilinear hysteretic strain hardening oscillators to typical near-source accelerograms with forward-directivity signatures without resorting to non-linear response history analysis (NRHA). In particular, the considered stochastic PLGM model is parametrically defined by a non-separable non-stationary stochastic process treating the high and the low frequency content of typical PLGMs in a consistent manner as a superposition of “bursts” of energy on the time-frequency plane with different amplitude, duration, bandwidth, location in time, and location in frequency. Each such burst is represented by a uniformly modulated non-stationary process of the separable kind. Further, the adopted stochastic dynamics formulation yields time-varying equivalent linear properties (ELPs) which are construed as non-stationary stochastic processes with evolutionary statistics dependent on the timeevolving intensity and frequency content of the PLGM stochastic excitation. It is numerically demonstrated by considering a PLGM stochastic process fitted to a typical fault-normal recorded accelerogram with a single forward-directivity lowfrequency pulse that the ELPs derived by the proposed approach for various different bilinear oscillators are amenable to a clear physical interpretation: they can be viewed as instantaneous (time-varying) effective stiffness and viscous damping characterizing the time-varying inelastic response level/behavior whose severity is governed by resonance structural dynamics phenomena related to the input seismic energy distribution on the time-frequency plane and to the pre-yield natural period of the bilinear oscillators. Furthermore, it is verified in the context of Monte Carlo analysis pertaining to an ensemble of 250 simulated PLGM records compatible with the adopted PLGM stochastic model that the peak inelastic response of bilinear oscillators can be well approximated by the peak response of equivalent linear oscillators defined by appropriate statistics of ELPs evaluated at the time instant when the response variance determined by the adopted approach is maximized. Overall, the herein reported numerical data illustrates the usefulness and applicability of the proposed approach to serve as a potent alternative tool in assessing the seismic vulnerability of yielding structures to PLGMs within the performance-based earthquake engineering framework compared to the currently used approaches relying on NRHA. At first instance, the herein presented approach can be adopted within a stochastic incremental dynamic analysis context to account for the influence of forward-directivity effects to seismic structural response.

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