Combination of Spectral Representation and Wavelet Packets for Generating Long-Period Ground Motions

Far-field long-period ground motions (hereafter long-period ground motions) featuring low-frequency components are responsible for the resonant responses of high-rise buildings. In this context, it is beneficial to assess the dynamic performance of these buildings under long-period ground motions with the aid of time history analysis. This paper proposes a method for generating long-period motions by combining long-period components synthesized by spectral representation with high-frequency components simulated by wavelet packets. Later-arriving long-period surface waves (LALP surface waves), which are determined on the grounds of phase dispersion, represent the main long-period properties in sense of velocity spectrum at longer periods of interest. An analytical expression for power spectrum density is employed to capture the narrowband properties of LALP velocity surface waves. Meanwhile, modification of the Gaussian random process is performed in time and frequency domains to attain a modulated initial seed motion, which shows the variability of the targeted ground motion. A simulation of high-frequency components is accomplished by means of iteration, in which wavelet coefficients of the modulated seed motion are adjusted to match the targeted response spectrum and cumulative energy plot. Furthermore, comparisons between an ensemble of realizations and target motions demonstrate the feasibility of the proposed method to generate long-period simulations sharing similar properties to target motions.

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