On the buckling of an elastic rotating beam

Stanislaw D. Furta, Wolfhard Kliem, Christian Pommer

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    Abstract

    A nonlinear model is developed, which describes the buckling phenomena of an elastic beam clamped to the interior of a rotating wheel. We use a power series method to obtain an approximate expression of the buckling equation and compare this with previous results in the literature. The linearized problem is integrated and this results in a second order differential equation of the Fuchs type, which allows an asymptotic expansion of the buckling equation. By means of Lyapunov and Chetaev functions, a rigorous proof is given that the loss of stability of the trivial equilibrium shape occurs for any length of the beam provided the angular velocity of the rotating wheel is sufficiently large. Finally we discuss the nonlinear problem and describe the qualitative behaviour of branches in a bifurcation diagram.
    Original languageEnglish
    JournalEuropean Journal of Mechanics A - Solids
    Volume16
    Issue number2
    Pages (from-to)307-324
    ISSN0997-7538
    Publication statusPublished - 1997

    Cite this

    Furta, S. D., Kliem, W., & Pommer, C. (1997). On the buckling of an elastic rotating beam. European Journal of Mechanics A - Solids, 16(2), 307-324.