Laplace- and Frequency-Domain Methods on Computing Transient Responses of Oscillators with Hysteretic Dampings to Deterministic Loading

Abstract

Efficiently computing the transient response of a linear hysteretic damping (LHD) system that is noncausal to deterministic loading that is regular or irregular is challenging. In this study, we developed a time-shifting causalization procedure and efficient solution methods to compute the transient response, conducted in the frequency or Laplace domain based on pole-residue operations. Because these operations require the causalized system’s transfer function to be in its pole-residue form, true poles were extracted by the Prony-SS method for the Laplace-domain method. In contrast, the frequency-domain method designates imaginary poles directly from the system’s frequency response function. Overall, the latter method was easier to implement and more computationally efficient but less capable of computing longer responses due to the imposition of the periodic oscillator. The proposed methods were used in numerical studies for oscillators with hysteretic damping and mixed viscous-hysteretic damping to earthquake-induced loading; correctness was verified by a time-domain method.