We characterize the complex, heavy-tailed probability density functions (pdfs) describing the response and its local extrema for structural systems subject to random forcing that includes extreme events. Our approach is based on recent probabilistic decomposition-synthesis (PDS) technique (Mohamad, M. A., Cousins, W., and Sapsis, T. P., 2016, “A Probabilistic Decomposition-Synthesis Method for the Quantification of Rare Events Due to Internal Instabilities,” J. Comput. Phys., 322, pp. 288–308), where we decouple rare event regimes from background fluctuations. The result of the analysis has the form of a semi-analytical approximation formula for the pdf of the response (displacement, velocity, and acceleration) and the pdf of the local extrema. For special limiting cases (lightly damped or heavily damped systems), our analysis provides fully analytical approximations. We also demonstrate how the method can be applied to high dimensional structural systems through a two-degrees-of-freedom (TDOF) example system undergoing extreme events due to intermittent forcing. The derived formulas can be evaluated with very small computational cost and are shown to accurately capture the complicated heavy-tailed and asymmetrical features in the probability distribution many standard deviations away from the mean, through comparisons with expensive Monte Carlo simulations.
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September 2018
Research-Article
Heavy-Tailed Response of Structural Systems Subjected to Stochastic Excitation Containing Extreme Forcing Events
Han Kyul Joo
,
Han Kyul Joo
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139
Search for other works by this author on:
Mustafa A. Mohamad
,
Mustafa A. Mohamad
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139
Search for other works by this author on:
Themistoklis P. Sapsis
Themistoklis P. Sapsis
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139
e-mail: sapsis@mit.edu
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139
e-mail: sapsis@mit.edu
Search for other works by this author on:
Han Kyul Joo
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139
Mustafa A. Mohamad
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139
Themistoklis P. Sapsis
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139
e-mail: sapsis@mit.edu
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139
e-mail: sapsis@mit.edu
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 17, 2017; final manuscript received February 2, 2018; published online July 26, 2018. Assoc. Editor: Dumitru Baleanu.
J. Comput. Nonlinear Dynam. Sep 2018, 13(9): 090914 (12 pages)
Published Online: July 26, 2018
Article history
Received:
August 17, 2017
Revised:
February 2, 2018
Citation
Kyul Joo, H., Mohamad, M. A., and Sapsis, T. P. (July 26, 2018). "Heavy-Tailed Response of Structural Systems Subjected to Stochastic Excitation Containing Extreme Forcing Events." ASME. J. Comput. Nonlinear Dynam. September 2018; 13(9): 090914. https://doi.org/10.1115/1.4039309
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