Nonlinear deformations of a slender rod rotated at one end

  • C. Y. Wang
Original Papers

Summary

A thin elastic rod is rotated at one end. The nonlinear deformations due to centrifugal forces are studied. The problem is governed by a nondimensional parameterJ which signifies the relative importance of rotation to flexibility, and the angle a between the rotation axis and the clamped end. The nonlinear differential equations are solved by three different perturbations and also numerical integration for the rangeJ5. Force, moment and displacement characteristics are determined. The solutions are unique for smallJ. Three solutions are possible, one may be unstable, for largerJ. Catastrophic changes may occur whenJ is decreased.

Keywords

Differential Equation Mathematical Method Rotation Axis Centrifugal Force Nonlinear Differential Equation 

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References

  1. [1]
    F. Odeh and I. Tadjbakhsh,A nonlinear eigenvalue problem for rotating rods. Arch. Rat. Mech. Anal.20, 81–94 (1965).Google Scholar
  2. [2]
    C. Y. Wang,On the bifurcation solutions of an axially rotating rod. Quart. J. Mech. Appl. Math.35, 391–402 (1982).Google Scholar

Copyright information

© Birkhäuser Verlag 1990

Authors and Affiliations

  • C. Y. Wang
    • 1
  1. 1.Michigan State UniversityEast LansingUSA

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