Dynamic bifurcation of a column when vertically impacting on a rigid plane

Abstract

The dynamic bifurcation of a column is investigated when it impacts a rigid plane vertically, which is completely different from the classical Eulerian static buckling. The variation law of the dimensionless critical buckling time with the dimensionless impact velocity is investigated, and the difference in dimensionless critical buckling times between columns without gravity and those with gravity is investigated. The concept of the dimensionless critical buckling velocity is proposed, which is the dimensionless form of the minimum velocity at which a column can buckle. Regardless of the different perspectives considered, the findings of the study show that either the dimensionless critical buckling time or the dimensionless critical buckling velocity can be used to determine whether buckling has occurred. The dimensionless displacement response of the column is calculated at the first contact between the column and the rigid plane. Different dimensionless initial defects in the column will result in different dimensionless displacement responses. The nonlinear effect has some influence on the analysis results.