SOLUTION OF THE FIRST PASSAGE PROBLEM FOR SIMPLE LINEAR AND NONLINEAR OSCILLATORS BY THE FINITE ELEMENT METHOD.

Lawrence Bergman, B. F. Spencer

Research output: Contribution to journalArticlepeer-review

Abstract

The problem of determining the probability that a structure becomes unsafe under random excitation over a given period of time is addressed. The excitation is modeled as zero mean Gaussian white noise, and the structure is modeled as a simple oscillator: linear, hardening Duffing, VanderPol, and power-law damped. Failure corresponds to first exceedance of symmetrically disposed absorbing barriers. This is the well known first passage problem in random vibration. A well posed initial-boundary value problem for the failure process is derived from Markov process theory and is solved by a Petrov-Galerkin finite element method. Also, a boundary value problem for the moments of the failure process is derived and similarly solved. Failure of higher dimensional systems is reviewed, and a modal technique is proposed to compute a conservative bound to the failure distribution. Also, the temporal effects of dynamic load combinations on simple system reliability are studied by modulating the white noise excitation. In the Bibliography, 86 citations are to first passage and related problems in random vibration; 9 additional citations are characterized as general references. 95 refs.

Original languageEnglish (US)
JournalT.&A.M. Report (University of Illinois at Urbana - Champaign, Department of Theoretical and Applie
Issue number461
StatePublished - Jan 1 1983
Externally publishedYes

ASJC Scopus subject areas

  • Engineering(all)

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