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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. [ABSTRACT FROM AUTHOR]

In evaluating of the response of linear systems to arbitrary intermittent loadings, traditional methods have been exclusively conducted in the time domain where the time resolution must be carefully chosen. In this paper, an accurate and efficient Laplace-time domain method is developed to perform the dynamic analysis of multi-degree-of-freedom (MDOF) systems to arbitrary intermittent loadings. The proposed method is a Laplace-time domain approach in the sense that (1) for each individual nonzero segment of an intermittent loading, the computation for the corresponding response is carried out in the Laplace domain (complex plane) by using algebraic pole-residue operations, and (2) for the total response calculation that accounts for all segments of intermittent loadings, the principle of linear superposition is applied in the time domain. Three numerical examples ranging from single-degree-of-freedom (SDOF) to 600-degree-of-freedom (DOF) systems are provided in this paper. Through numerical examples, this study demonstrates the superiority of the proposed method over traditional time-domain methods in terms of both accuracy and computational efficiency. [ABSTRACT FROM AUTHOR]

Evaluating the mean-square response at the transient state of a single degree of freedom (SDOF) system to stationary random excitation has been extensively studied in the past, but the explicit closed-form solution has not been available unless the excitation was considered to be a physically unrealizable white noise process. In this paper, explicit closed-form solutions for the mean-square response are derived for arbitrary input power spectral density (psd) functions. While all existing solution methods for evaluating the mean-square response have always been conducted in the time and/or frequency domains, the proposed method is operated in the complex plane (Laplace domain) based on pole-residue formulations. Not only is the proposed approach is much more efficient than other existing approaches, but also meaningful physical and mathematical insights can be gained in its solution procedure. To demonstrate the procedure, this paper considers the excitation process characterized by a white and nonwhite psd, respectively, and the corresponding closed-form solutions for the transient mean-square response of SDOF systems are derived. The correctness of the closed-form solution for the nonwhite psd is verified by Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Systems of second-order linear ordinary differential equations (ODEs) to arbitrary input functions appear in many fields of physics and engineering. Numerical methods for solving these kinds of problems have been mainly performed in the time and frequency domains. In contrast, this paper develops an efficient, seminumerical pole-residue method implemented in the Laplace domain. In this article, a key concept and development is on how to compute the poles and residues of the output from those of the input and system transfer functions. Once the poles and residues of the output are known, the corresponding time history of the output is readily obtained. Even though the correctness of the new method has been verified by using a step-by-step time-domain solution, the accuracy of the new method in theory is higher than that of any time-domain approach, partially because the output obtained from the new method is a continuous function of time. [ABSTRACT FROM AUTHOR]