Wavelet-Based Mean Instantaneous Period (MIP) of Ground Motions and Time-Varying Period Elongation of Earthquake Excited Hysteretic Structures

The time-dependent wavelet-based mean instantaneous period (MIP) is used as a numerical tool to characterize the time-varying frequency content of typical far-field recorded earthquake ground motions (GMs) and to probe into the hysteretic response of reinforced concrete (r/c) yielding structures. It is shown that the MIP captures well the temporal change of the average frequency content of GMs towards lower frequencies by considering the MIPs of 20 scenario earthquake GMs derived using two different wavelet families. It is further argued that the MIP can be viewed as a generalization of the Fourier-based mean period T_m widely used to characterize the stationary/average frequency content of GMs. This argument is based on the observation that temporal averaged MIPs lie reasonably close to T_m for judicially defined harmonic wavelet bases. Moreover, MIPs of acceleration response signals are examined derived from incremental dynamic analysis applied to a hysteretic oscillator representing a benchmark 12-storey r/c frame for the above suite of GMs. It is observed that the response signal MIPs tend to converge to the GM MIP in a point-wise manner as stronger inelastic behaviour is exhibited. Further, it is shown that the slope of the ensemble average MIP for the near-collapse limit state lies close to the ensemble average GM MIP, while it may also be treated as indicator of the so-called “period elongation” phenomenon for degrading inelastic structures. Overall, the reported numerical data evidence the potential of the slope of the MIP as a record selection criterion accounting for the influence of the time-varying frequency content of GMs to structural response within the performance-based earthquake engineering framework.