An Integral Equation Method for the First-Passage Problem in Random Vibration

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    The first-passage problem for a nonstationary stochastic process is formulated as an integral identity, which produces known bounds and series expansions as special cases, while approximation of the kernel leads to an integral equation for the first-passage probability density function. An accurate, explicit approximation formula for the kernel is derived, and the influence of uni or multi modal frequency content of the process is investigated. Numerical results provide comparisons with simulation results and alternative methods for narrow band processes, and also the case of a multimodal, nonstationary process is dealt with.
    Original languageEnglish
    JournalJournal of Applied Mechanics
    Volume51
    Issue number3
    Pages (from-to)674-679
    ISSN0021-8936
    DOIs
    Publication statusPublished - 1984

    Cite this

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    title = "An Integral Equation Method for the First-Passage Problem in Random Vibration",
    abstract = "The first-passage problem for a nonstationary stochastic process is formulated as an integral identity, which produces known bounds and series expansions as special cases, while approximation of the kernel leads to an integral equation for the first-passage probability density function. An accurate, explicit approximation formula for the kernel is derived, and the influence of uni or multi modal frequency content of the process is investigated. Numerical results provide comparisons with simulation results and alternative methods for narrow band processes, and also the case of a multimodal, nonstationary process is dealt with.",
    author = "Madsen, {Peter Hauge} and Steen Krenk",
    year = "1984",
    doi = "10.1115/1.3167691",
    language = "English",
    volume = "51",
    pages = "674--679",
    journal = "Journal of Applied Mechanics",
    issn = "0021-8936",
    publisher = "American Society of Mechanical Engineers",
    number = "3",

    }

    An Integral Equation Method for the First-Passage Problem in Random Vibration. / Madsen, Peter Hauge; Krenk, Steen.

    In: Journal of Applied Mechanics, Vol. 51, No. 3, 1984, p. 674-679.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - An Integral Equation Method for the First-Passage Problem in Random Vibration

    AU - Madsen, Peter Hauge

    AU - Krenk, Steen

    PY - 1984

    Y1 - 1984

    N2 - The first-passage problem for a nonstationary stochastic process is formulated as an integral identity, which produces known bounds and series expansions as special cases, while approximation of the kernel leads to an integral equation for the first-passage probability density function. An accurate, explicit approximation formula for the kernel is derived, and the influence of uni or multi modal frequency content of the process is investigated. Numerical results provide comparisons with simulation results and alternative methods for narrow band processes, and also the case of a multimodal, nonstationary process is dealt with.

    AB - The first-passage problem for a nonstationary stochastic process is formulated as an integral identity, which produces known bounds and series expansions as special cases, while approximation of the kernel leads to an integral equation for the first-passage probability density function. An accurate, explicit approximation formula for the kernel is derived, and the influence of uni or multi modal frequency content of the process is investigated. Numerical results provide comparisons with simulation results and alternative methods for narrow band processes, and also the case of a multimodal, nonstationary process is dealt with.

    U2 - 10.1115/1.3167691

    DO - 10.1115/1.3167691

    M3 - Journal article

    VL - 51

    SP - 674

    EP - 679

    JO - Journal of Applied Mechanics

    JF - Journal of Applied Mechanics

    SN - 0021-8936

    IS - 3

    ER -