On stochastic dynamic analysis and assessment of bistable structures

  • Xianbo Sun
  • Yahui ZhangEmail author
  • David Kennedy
Original Paper


This paper investigates some basic issues on the stochastic dynamic analysis and assessment of bistable structures from an applications perspective, illustrated with a classical spring–mass–rod structure. A complete Lagrangian-description-based Monte Carlo simulation and an Eulerian-description-based Fokker–Planck equation analysis are implemented, respectively, to capture the evolution process of the physical response probability density function, with special focus on the dynamics under the statistical steady state condition. A comparison of these two methods outlines their capabilities. As a representative example, quantitative counting and statistical analysis of the number and amplitudes of snapping-through of the structure indicate that physical quantities for structural assessment may show certain statistical regularities under the statistical steady state condition, which can be utilized efficiently to reduce the efforts of structural assessment without loss of precision.


Bistable structures Monte Carlo simulation Fokker–Planck equation Statistical steady state Probability density evolution 



The authors are grateful for support under grants from the National Science Foundation of China (11672060) and the Cardiff University Advanced Chinese Engineering Centre.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, International Center for Computational MechanicsDalian University of TechnologyDalianPeople’s Republic of China
  2. 2.School of EngineeringCardiff UniversityCardiffUK
  3. 3.State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and MechanicsDalian University of TechnologyDalianPeople’s Republic of China

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