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    Reliability of Uncertain Linear and Nonlinear Systems

    Source: Journal of Engineering Mechanics:;1988:;Volume ( 114 ):;issue: 001
    Author:
    B. F. Spencer, Jr.
    ,
    I. Elishakoff
    DOI: 10.1061/(ASCE)0733-9399(1988)114:1(135)
    Publisher: American Society of Civil Engineers
    Abstract: The reliability of uncertain single degree‐of‐freedom linear and nonlinear systems subjected to broadband random excitation is examined. A robust Petrov‐Galerkin finite element solution for the reliability of deterministic single degree‐of‐freedom systems is used in conjunction with the theorem of total probability and a numerical integration scheme to obtain the sought reliabilities. Particular examples are given for the linear system in which the stiffness is modeled as a discrete random variable or as a continuous random variable. Use of the mean stiffness in an analysis is shown to be generally unconservative in the region of design interest, whereas using the Poisson approximation in conjunction with the moments of first passage time indicates that the results should be conservative. A particular example is given in which the error introduced by using the mean system parameters in the analysis is increased by increasing the failure bound width. A final example is given for the Duffing oscillator.
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      Reliability of Uncertain Linear and Nonlinear Systems

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    contributor authorB. F. Spencer, Jr.
    contributor authorI. Elishakoff
    date accessioned2017-05-08T22:18:55Z
    date available2017-05-08T22:18:55Z
    date copyrightJanuary 1988
    date issued1988
    identifier other%28asce%290733-9399%281988%29114%3A1%28135%29.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/77309
    description abstractThe reliability of uncertain single degree‐of‐freedom linear and nonlinear systems subjected to broadband random excitation is examined. A robust Petrov‐Galerkin finite element solution for the reliability of deterministic single degree‐of‐freedom systems is used in conjunction with the theorem of total probability and a numerical integration scheme to obtain the sought reliabilities. Particular examples are given for the linear system in which the stiffness is modeled as a discrete random variable or as a continuous random variable. Use of the mean stiffness in an analysis is shown to be generally unconservative in the region of design interest, whereas using the Poisson approximation in conjunction with the moments of first passage time indicates that the results should be conservative. A particular example is given in which the error introduced by using the mean system parameters in the analysis is increased by increasing the failure bound width. A final example is given for the Duffing oscillator.
    publisherAmerican Society of Civil Engineers
    titleReliability of Uncertain Linear and Nonlinear Systems
    typeJournal Paper
    journal volume114
    journal issue1
    journal titleJournal of Engineering Mechanics
    identifier doi10.1061/(ASCE)0733-9399(1988)114:1(135)
    treeJournal of Engineering Mechanics:;1988:;Volume ( 114 ):;issue: 001
    contenttypeFulltext
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