Structural model for the dynamic buckling of a column under constant rate compression

Dynamic buckling behavior of a column (rod, beam) under constant rate compression is considered. The buckling is caused by prescribed motion of column ends toward each other with constant velocity. Simple model with one degree of freedom simulating static and dynamic buckling of a column is derived. In the case of small initial disturbances the model yields simple analytical dependencies between the main parameters of the problem: critical force, compression rate, and initial disturbance. It is shown that the time required for buckling is inversely proportional to cubic root of compression velocity and logarithmically depends on the initial disturbance. Analytical expression for critical buckling force as a function of compression velocity is derived. It is shown that in a range of compression rates typical for laboratory experiments the dependence is accurately approximated by a power law with exponent close to 2/3. Theoretical findings are supported by available results of laboratory experiments. Keywords: dynamic buckling, Hoff problem, column, Airy equation, Euler force.