Frequency domain study of the equivalent pulse models of near-fault ground motions with forward directivity

There is a growing recognition that a time history representation is better able to capture the effects of near-fault ground motions on structures. However, for the lack of quantitative knowledge on the relationship of equivalent pules, the results of studies on the response of structures to near-fault ground motions with different equivalent pules can not be united. Different equivalent pules produce variations in the response of a structure. 3 simple equivalent pulses that widely used to characterize the forward-directivity effects are considered. The quantitative knowledge on the relationship of equivalent pules is presented. It is shown that the amplitude ratio of frequency components keep constant in a equivalent pules model. The amplitude ratio of the same frequency components in different equivalent models with the same pulse period keep constant. The difference of frequency components between sine-wave equivalent pulse and triangular equivalent pulse is not obvious. However, frequency components of rectangular pulse significantly different from sine-wave and triangular equivalent pulse. The energy of rectangular equivalent pulse concentrates in odd term frequencies of equivalent pules. The concentration can result in significant difference between the seismic responses of structures subjected to rectangular equivalent pulse and the seismic responses induced by other equivalent pulses.