First passage time for linear systems with stochastic coefficients

L. A. Bergman, B. F. Spencer

Research output: Contribution to journalArticlepeer-review


The moments of time to first passage of a second order linear system with stochastic coefficients and loading are determined by formulating and solving the Pontryagin-Vitt equations, a recursive system of boundary value problems. Solution is by a Petrov-Galerkin finite element method, and the first two ordinary moments are computed. A pin-ended beam-column subjected to simultaneous axial and transverse loading is examined, and the results obtained are compared with those of Monte Carlo simulation. Conclusions are drawn regarding the relative importance of the two loads upon the failure process as well as of the effects of cross-correlation between the loads.

Original languageEnglish (US)
Pages (from-to)46-53
Number of pages8
JournalProbabilistic Engineering Mechanics
Issue number1
StatePublished - Mar 1987
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Civil and Structural Engineering
  • Nuclear Energy and Engineering
  • Condensed Matter Physics
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering


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