The steady state free vibrations of pin-ended steel columns in the elastic range are analysed by direct minimisation of an energy function. The columns are subjected to either constant axial compressive force, or constant axial shortening, and the (lateral) amplitude of vibration is prescribed. The analysis includes lateral deflections of magnitude comparable to the cross-section depth, and so is nonlinear. The columns can either be initially straight, or can have an initial sinusoidal geometric imperfection of magnitude Delta_o. The energy function employed is based on the function presented by the author in previous work to analyse the static collapse behaviour of such columns; the current function incorporates additional terms corresponding to the dynamic effects. The analysis is rapid, and is shown to give accurate results for the classical linear vibration problem. Results for initially imperfect columns demonstrate the significant effect of the manner in which the axial load is applied.

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