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      A Novel Approach for Evaluating Nonstationary Response of Dynamic Systems to Stochastic Excitation

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          The transient state of a dynamic system, such as offshore structures, to random excitation is always nonstationary. Many studies have contributed to evaluating response covariances at the transient state of a linear multi-degree-of-freedom (MDOF) system to random excitations, but a closed-form solution was not available unless the excitation was assumed to be a physically unrealizable white noise process. This study derives explicit, closed-form solutions for the response covariances at the transient state by using a pole-residue (PR) approach operated in the Laplace domain when the excitations are assumed to be stationary random processes described by physically realizable spectral density functions. By using the PR method, we can analytically solve the triple integral in evaluating the nonstationary response covariance. As this approach uses the poles and residues of system transfer functions, rather than the conventional mode superposition technique, the method is applicable to MDOF systems with non-classical damping models. Particular application of the proposed method is demonstrated for multi-story shear buildings to stochastic ground acceleration characterized by the Kanai–Tajimi spectral density function model, and a numerical example is provided to illustrate the detailed steps. No numerical integrations are required for computing the response covariances as the exact closed-form solution has been derived. The correctness of the proposed method is numerically verified by Monte Carlo simulations.

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          Author and article information

          Journal of Ocean University of China
          Science Press and Springer (China )
          10 July 2020
          01 August 2020
          : 19
          : 4
          : 781-789
          1College of Engineering, Ocean University of China, Qingdao 266100, China
          2Department of Ocean Engineering, University of Rhode Island, Narragansett, RI 02882, USA
          3College of Engineering, University of Rhode Island, Kingston, RI 02881, USA
          Author notes
          *Corresponding author: HU Sau-Lon James, E-mail: jameshu@
          Copyright © Ocean University of China, Science Press and Springer-Verlag GmbH Germany 2020.

          The copyright to this article, including any graphic elements therein (e.g. illustrations, charts, moving images), is hereby assigned for good and valuable consideration to the editorial office of Journal of Ocean University of China, Science Press and Springer effective if and when the article is accepted for publication and to the extent assignable if assignability is restricted for by applicable law or regulations (e.g. for U.S. government or crown employees).

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