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Vibrations of a rotating flexible rod clamped off the axis of rotation

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Summary

We consider a fourth-order boundary value problem associated with the small vibrations of a uniform flexible rod which is clamped at one end and rotates in a plane perpendicular to the axis of rotation. A significant feature is that the axis of rotation does not pass through the clamped end itself. For rapid rotation rates, the governing equation involves a small parameter and must be treated by singular perturbation techniques. A second parameter fixes the relative location of two turning points. For a range of this second parameter, consistent approximations to the characteristic equation are derived, and the limiting behavior of the eigenvalues is obtained.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, M5S 1A1, Toronto, Canada

    W. D. Lakin

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  1. W. D. Lakin
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Lakin, W.D. Vibrations of a rotating flexible rod clamped off the axis of rotation. J Eng Math 10, 313–321 (1976). https://doi.org/10.1007/BF01535567

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  • DOI: https://doi.org/10.1007/BF01535567

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