A dynamic buckling geometric approach of 2-DOF autonomous potential lumped-mass systems under impact loading

Abstract Dynamic buckling for autonomous nondissipative lumped-mass systems under impact loading is thoroughly investigated. It is assumed that a fully plastic impact due to a striking body falling freely from a given height takes place, and that the effect of wave propagation can be neglected. Attention is focused on the post-impact dynamic buckling after establishing the initial velocities and the associated initial kinetic energy. Via a thorough discussion of the dynamic buckling mechanism based on certain salient geometric features of the total potential energy surface, one can obtain practically “exact” dynamic buckling loads, by extending previous findings valid for step load of infinite duration to the case of impact load. The proposed geometric approach, which is described for n -DOF systems and then presented in detail for 2-DOF systems, gives comprehensive, direct, readily obtained and reliable solutions compared to numerical integration schemes.

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