Response of Non-Linear Systems to Renewal Impulses by Path Integration

Søren R.K. Nielsen, R. Iwankiewicz

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    Abstract

    The cell-to-cell mapping (path integration) technique has been devised for MDOF non-linear and non-hysteretic systems subjected to random trains of impulses driven by an ordinary renewal point process with gamma-distributed integer parameter interarrival times (an Erlang process). Since the renewal point process has not independent increments the state vector of the system, consisting of the generalized displacements and velocities, is not a Markov process. Initially it is shown how the indicated systems can be converted to an equivalent Poisson driven system at the expense of introducing additional discrete-valued state variables for which the stochastic equations are also formulated.
    Original languageEnglish
    Place of PublicationAalborg
    PublisherDept. of Building Technology and Structural Engineering
    Number of pages23
    Publication statusPublished - 1995
    SeriesStructural Reliability Theory
    Number142
    VolumeR9512
    ISSN0902-7513

    Bibliographical note

    Submitted to ASCE, Journal of Engineering Mechanics

    PDF for print: 32 pp.

    Keywords

    • Non-Linear Systems
    • Random Vibration
    • Random Impulses
    • Renewal Point Process
    • Path Integration
    • Cell-to-Cell Mapping

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