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.
Skip Nav Destination
Article navigation
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
Download citation file:
Get Email Alerts
Cited By
Semi-Implicit Integration and Data-Driven Model Order Reduction in Structural Dynamics With Hysteresis
J. Comput. Nonlinear Dynam (May 2023)
Define the Lyapunov Exponents for ψ-Fractional Differential System
J. Comput. Nonlinear Dynam (May 2023)
Equivalent Beam Model and Improved Structure Design of Large Space Antenna Truss With Geometric Nonlinearity
J. Comput. Nonlinear Dynam (May 2023)
Unconditionally Stable Numerical Scheme for Heat Transfer of Mixed Convective Darcy–Forchheimer Flow of Micropolar Fluid Over Oscillatory Moving Sheet
J. Comput. Nonlinear Dynam (April 2023)
Related Articles
Lyapunov Exponents and Stochastic Stability of Two-Dimensional Parametrically Excited Random Systems
J. Appl. Mech (September,1993)
Weak Form Quadrature Element Method and Its Applications in Science and Engineering: A State-of-the-Art Review
Appl. Mech. Rev (May,2017)
New Conservation Laws, Lagrangian Forms, and Exact Solutions of Modified Emden Equation
J. Comput. Nonlinear Dynam (July,2017)
Related Proceedings Papers
Related Chapters
Stability for a Class of Infinite Dimension Stochastic Systems with Delay
International Conference on Computer Technology and Development, 3rd (ICCTD 2011)
Advances in the Stochastic Modeling of Constitutive Laws at Small and Finite Strains
Advances in Computers and Information in Engineering Research, Volume 2
Introduction
Computer Vision for Structural Dynamics and Health Monitoring