  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.
