The calculation of the nonlinear time-response of structures such as RC (reinforced concrete) frames to base excitation such as earthquake waves is vital to ensure the safety of structures. Of course the response changes significantly with the applied base excitation. The usual approaches to compare the different earthquake waves are based on non-localized spectra, such as response spectra and power spectra, which do not contain any time information. However these non-localized spectra often do not explain the large difference between structural responses, and are not able to reflect all of the characteristics of the earthquake waves. Local spectra, which can be easily obtained by the wavelet transform, calculate the energy distribution of the waves in the time-frequency domain. Using the wavelet transform it is easy to see the differences in the energy distribution via the local spectra of each wave, and therefore to understand the very different structural responses. Hence the time-frequency distribution of the wave energy should be taken into account during the selection of earthquake waves to apply to structural models to determine the nonlinear time response.

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