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Vibration and buckling of rotating flexible rods at transitional parameter values

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Summary

We consider the connection between vibration and buckling problems for a uniform flexible rod which is clamped at one end and rotates in a plane perpendicular to the axis of rotation. The rod is assumed off-clamped, i.e. the axis of rotation does not pass through the rod's clamped end. The resulting fourth-order boundary value problem with a turning point for the free vibrations is solved using uniform approximations in a transitional parameter range where high rotation rates balance small off-clampings. Second approximations to the vibration eigenvalues are used to determine critical buckling rotation rates for the slightly off-clamped rods. Buckling is unexpected in this situation as the rod is wholly under tension.

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Authors and Affiliations

  1. Department of Mathematical and Computing Sciences, Old Dominion University, 23508, Norfolk, Virginia, USA

    W. D. Lakin & A. Nachman

Authors
  1. W. D. Lakin
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  2. A. Nachman
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Lakin, W.D., Nachman, A. Vibration and buckling of rotating flexible rods at transitional parameter values. J Eng Math 13, 339–346 (1979). https://doi.org/10.1007/BF00037540

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  • DOI: https://doi.org/10.1007/BF00037540

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