The equations for small amplitude motions of a slender beam with a prescribed axial motion is derived from Hamilton's principle. It is shown that under a particular set of conditions this equation admits a closed form similarity solution. For other conditions approximate solutions are obtained by the modal approach. Through a transformation it is shown that the problem may be changed to one of fixed domain. Finally the analysis is extended to large amplitude oscillations using the co-rotational nonlinear finite element formulation.
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