Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods

Søren R.K. Nielsen, John Dalsgaard Sørensen

Research output: Book/ReportReportResearch

353 Downloads (Pure)

Abstract

Close approximations to the first passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first passage probability density function and the distribution function for the time interval spent below a barrier before outcrossing. An integral equation for the probability density function of the time interval is formulated, and adequate approximations for the kernel are suggested. The kernel approximation results in approximate solutions for the probability density function of the time interval, and hence for the first passage probability density. The results of the theory agree well with simulation results for narrow banded processes dominated by a single frequency, as well as for bimodal processes with 2 dominating frequencies in the structural response.
Original languageEnglish
PublisherInstitut for Bygningsteknik, Aalborg Universitetscenter
Number of pages16
Publication statusPublished - 1986
SeriesStructural Reliability Theory
NumberR8618
Volume21
ISSN0105-7421

    Fingerprint

Keywords

  • Random Vibration
  • Stochastic Processes
  • First Passage Failure
  • Bimodal Processes
  • Integral Equations

Cite this

Nielsen, S. R. K., & Sørensen, J. D. (1986). Approximations to the Probability of Failure in Random Vibration by Integral Equation Methods. Institut for Bygningsteknik, Aalborg Universitetscenter. Structural Reliability Theory , No. R8618, Vol.. 21