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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.
Subject(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.
Issue Date:1983-11
Publisher:Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report:TAM R 461
1983-6007
Genre:Technical Report
Type:Text
Language:English
URI:http://hdl.handle.net/2142/112200
ISSN:0073-5264
Sponsor:National Science Foundation 83/11 NSF NEA 80 23263 83/11
Rights Information:Copyright 1983 Board of Trustees of the University of Illinois
Date Available in IDEALS:2021-11-04


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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    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.

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