On stochastic dynamic analysis and assessment of bistable structures

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