An approximate method for determining the static deflection and natural frequency of a cracked beam

Tianxin Zheng, Tianjian Ji

    Research output: Contribution to journalArticlepeer-review

    Abstract

    This paper provides an approximate method to determine the stiffness and the fundamental frequency of a cracked beam. The cracked beam is first represented as an un-cracked beam with equivalent reduced sections around the cracks. The effect of the cracks is explained, visualised and quantified using the equivalence concept developed for stepped beams with periodically variable cross-sections. Then an alternative expression of the improved Rayleigh method is provided to calculate the natural frequencies of a beam with a variable stiffness distribution along its length. As the method is insensitive to the assumed mode shapes, it avoids the difficulty in choosing appropriate mode shapes and yields accurate results. This is shown using several examples to compare the results determined using the proposed method and the Finite Element method (FEM). The method greatly simplifies the calculation of cracked beams with complicated configurations, such as a beam with several cracks, a cracked beam with concentrated masses, a beam with cracks close to each other, and a beam with periodically distributed cracks. © 2012 Elsevier Ltd.
    Original languageEnglish
    Pages (from-to)2654-2670
    Number of pages16
    JournalJournal of Sound and Vibration
    Volume331
    Issue number11
    DOIs
    Publication statusPublished - 21 May 2012

    Keywords

    • cracked beams, equivalent beams, approximate methods, variable stiffness

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