Pulse extraction and displacement response evaluation for long-period ground motions

Long-period ground motions with directivity and/or path effects are often characterised by the presence of velocity and acceleration pulses in the lowermost frequency range. An objective of this article is to present a discrete-time signal processing method for isolating these pulses. In this method, the velocity and the acceleration pulses are identified by applying a low-pass discrete-time filter H_lp (ω) at a suitable cut-off frequency f _c to the Fourier transforms of the original velocity and acceleration ground motion time histories, respectively. Another objective of this article is to present a mathematical expression for evaluating the linear displacement response of a single degree-of-freedom (SDF) system by simultaneous application of two frequency modulators, H_lp (ω) and H_u (ω), to the original ground excitation. By using only the pulse component of the ground motion as the excitation force, it is shown that the displacement response of the SDF system with natural period exceeding a certain value referred to as the cut-off period T _c is quite comparable with that due to the original ground excitation. Also, for ground motions that contain multiple-period pulses, it is shown that the displacement response spectrum of the SDF system exhibits multiple peaks at different natural system periods T _n.