Numerical treatment of seismic accelerograms and of inelastic seismic structural responses using harmonic wavelets

The harmonic wavelet transform is employed to analyze various kinds of nonstationary signals common in aseismic design. The effectiveness of the harmonic wavelets for capturing the temporal evolution of the frequency content of strong ground motions is demonstrated. In this regard, a detailed study of important earthquake accelerograms is undertaken and smooth joint time-frequency spectra are provided for two near-field and two far-field records; inherent in this analysis is the concept of the mean instantaneous frequency. Furthermore, as a paradigm of usefulness for aseismic structural purposes, a similar analysis is conducted for the response of a 20-story steel frame benchmark building considering one of the four accelerograms scaled by appropriate factors as the excitation to simulate undamaged and severely damaged conditions for the structure. The resulting joint time-frequency representation of the response time histories captures the influence of nonlinearity on the variation of the effective natural frequencies of a structural system during the evolution of a seismic event. In this context, the potential of the harmonic wavelet transform as a detection tool for global structural damage is explored in conjunction with the concept of monitoring the mean instantaneous frequency of records of critical structural responses

Generating Realistic Ground Motions for Nonlinear Seismic Hazard Analysis — An Application to Hard Rock Sites in Eastern North America

This paper aims to determine the dependence of seismic response on the shape of the time-domain filter used in the stochastic method of ground motion prediction. Brune’s single-corner point source model was used in conjunction with the current attenuation relationships developed for hard rock sites in the Eastern North America (ENA) to obtain the target ground motion spectrum. A total of three hundred synthetic accelerograms were generated by filtering the Gaussian white noise with exponential, triangular and trapezoidal windows. For each accelerogram, displacement response of the Duffing’s oscillator was calculated, and its average amplitude spectrum was constructed in the joint time-frequency domain using Mexican hat wavelets. This procedure was repeated for three levels of nonlinearity. Among the three shapes examined, the trapezoidal window was associated with longer durations of sustained energy, thereby increasing the level of the expected damage. The dependence of the seismic response to the particular filter shape became more pronounced with increased levels of nonlinearity. This study concludes that ground motions with the same Fourier Amplitude Spectrum could cause substantially different levels of seismic damage on the same structure, depending on the time-frequency localization of the energy imparted to the structure

Wavelet analysis of nuclear magnetic resonance signal characteristics

The wavelet energy spectrum was proposed to analyze nuclear magnetic resonance signal characteristics. This paper focused on the intermolecular multiple quantum coherence and radiation damping signal for they had similar Fourier spectra. The free induced decay signals originating from the intermolecular double quantum coherence and radiation damping are demonstrated by both experiments and simulations. Compared with the Fourier spectrum, the wavelet energy spectrum revealed the signal intensity is not only relaled with time but also with frequency. Relevant characteristics of the wavelet energy spectrum, such as the maximum energy, the corresponding moment and the total energy were investigated in detail. As for intermolecular double quantum coherence, the maximum and total energy reaches the top it,hen the optimal flip angle is applied Moreover, the maximum Moments are the same irrespective of the different flip angles. With regard to radiation damping the energy achieves maximum when the flip angle is 90 degrees, and the larger the flip angle, is, the more the total energy is and the longer the acquiring moment is