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    On the Reliability of a Simple Hysteretic System

    Source: Journal of Engineering Mechanics:;1985:;Volume ( 111 ):;issue: 012
    Author:
    B. F. Spencer, Jr.
    ,
    L. A. Bergman
    DOI: 10.1061/(ASCE)0733-9399(1985)111:12(1502)
    Publisher: American Society of Civil Engineers
    Abstract: A method to determine statistical moments of time to first passage of a simple oscillator, incorporating the modified Bouc hysteresis model, has been developed. A generalized Pontriagin‐Vitt equation is formulated from Markov process theory and solved by a Petrov‐Galerkin finite element method. The resulting moments are given as functions of initial displacement and velocity of the oscillator, as well as of the initial hysteretic force in the oscillator. The first two moments are used in conjunction with a maximum entropy distribution to estimate the probability of failure of the oscillator. The accuracy and economy of the method is demonstrated for a particular example drawn from base isolation of a simple structure. A comparison of the finite element results with those obtained by Monte Carlo simulation is then given for this example.
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      On the Reliability of a Simple Hysteretic System

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    contributor authorB. F. Spencer, Jr.
    contributor authorL. A. Bergman
    date accessioned2017-05-08T22:12:18Z
    date available2017-05-08T22:12:18Z
    date copyrightDecember 1985
    date issued1985
    identifier other%28asce%290733-9399%281985%29111%3A12%281502%29.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/73496
    description abstractA method to determine statistical moments of time to first passage of a simple oscillator, incorporating the modified Bouc hysteresis model, has been developed. A generalized Pontriagin‐Vitt equation is formulated from Markov process theory and solved by a Petrov‐Galerkin finite element method. The resulting moments are given as functions of initial displacement and velocity of the oscillator, as well as of the initial hysteretic force in the oscillator. The first two moments are used in conjunction with a maximum entropy distribution to estimate the probability of failure of the oscillator. The accuracy and economy of the method is demonstrated for a particular example drawn from base isolation of a simple structure. A comparison of the finite element results with those obtained by Monte Carlo simulation is then given for this example.
    publisherAmerican Society of Civil Engineers
    titleOn the Reliability of a Simple Hysteretic System
    typeJournal Paper
    journal volume111
    journal issue12
    journal titleJournal of Engineering Mechanics
    identifier doi10.1061/(ASCE)0733-9399(1985)111:12(1502)
    treeJournal of Engineering Mechanics:;1985:;Volume ( 111 ):;issue: 012
    contenttypeFulltext
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