Dynamic bifurcation buckling of an impacted column

In this paper, the dynamic counterpart of the celebrated Euler buckling problem is formulated and solved by considering the case of a slender column that is impacted by a falling mass. We introduce a new notion, that of the time to buckle, “t∗”, which is the corresponding critical quantity analogous to the critical load in static Euler buckling. A set of experimental results previously presented by Gladden et al. [J.R. Gladden, N.Z. Handzy, A. Belmonte, E. Villermaux, Dynamic buckling and fragmentation in brittle rods, Physical Review Letters 94 (3) (2005) 035503], are used to illustrate the notions we introduce and as a means for comparison against the predictions of our work.