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Large amplitude whirling motions of a simply supported beam constrained to have a fixed length are investigated. Equations of motion taking into account bending in two planes and longitudinal deformations are developed. Using the method of harmonic balance, response curves for certain planar and non-planar steady state, forced motions are obtained. Another approximate scheme is used to study the stability of these motions. Stable regions corresponding to non-planar motions are found, thus confirming the existence of whirling motions. Numerical results are presented and discussed for several specific cases.

No abstract

Steady and unsteady free motions of compact beams with fixed ends are examined. It is found that in certain situations planar motions are unstable to out-of-plane perturbations and whirling motions occur. In resonant cases these whirling motions are of the beating type, whereas in non-resonant situations they have a steady-state behaviour.

The writer wishes to thank Edgar Thompson and Lloyd LeBlanc for their assistance in making the detailed spectral absorption coefficient calculations referred to in this note.