University of Illinois Urbana-Champaign

Solution on first passage problem for simple linear and nonlinear oscillators by finite element method

Bergman, Larry A.; Spencer, B. F. Jr.

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https://hdl.handle.net/2142/112200

Description

Title
Solution on first passage problem for simple linear and nonlinear oscillators by finite element method
Author(s)
  • Bergman, Larry A.
  • Spencer, B. F. Jr.
Issue Date
1983-11
Keyword(s)
  • First Passage Problem
  • Random Vibration
  • Linear & Nonlinear Systems
  • Structural Reliability
  • Stochastic Load Combination
  • Finite Element Method
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 model 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.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 461
  • 1983-6007
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112200
Sponsor(s)/Grant Number(s)
National Science Foundation 83/11 NSF NEA 80 23263 83/11
Copyright and License Information
Copyright 1983 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.