### 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 language | English |
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Journal | European Journal of Mechanics A - Solids |

Volume | 16 |

Issue number | 2 |

Pages (from-to) | 307-324 |

ISSN | 0997-7538 |

Publication status | Published - 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.