Abstract
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.
Highlights
Far-field long-period ground motions, which consist of dominant low-frequency components, are likely to enable high-rise buildings to excite resonance responses lasting several minutes [1]
Wavelet packets analysis is applied to the decomposition of a time series x(t) into a set of wavelet coefficients cij,k. is means that energy is localized in both time and frequency domains. e basic expression in the form of convolution is defined as follows:
The majority of coefficients at frequencies ranging from 4 to 7 Hz correspond to the peak values of the acceleration response spectrum in Figure 9(c); for temporal domain, the majority of coefficients occurring at approximately 100 sec correspond to a strong shocking phase during which the cumulative energy curve shows a sharp increase in Figure 9(d). is suggests that the wavelet packets transform has the potential to capture the characteristics pertaining to intensity and spectrum, each of which is well correlated with the time and frequency domains, respectively
Summary
Far-field long-period ground motions, which consist of dominant low-frequency components, are likely to enable high-rise buildings to excite resonance responses lasting several minutes [1]. E generation of ground motions compatible with a prescribed spectrum is attractive to engineers, since it is considered an extension of stochastic simulations In essence, this process modifies the amplitudes of Fourier components in the frequency domain to attain a realization which closely matches a given response spectrum [6, 7]. E objective of this paper is to generate long-period ground motions through spectral representation for generating long-period components and wavelet packets for simulating high-frequency components To achieve this aim, a time segment consisting of LALP components is truncated from acceleration time series on the basis of phase dispersion. Wavelet coefficients of the initial seed motion are adjusted by an iterative procedure to generate high-frequency components which are compatible with the target spectrum and cumulative energy plot. Comparisons of simulations with target motions demonstrate that the proposed method has the potential to generate ground motions sharing similar long-period characteristics with target motions
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