Twin-characteristic-parameter solution for dynamic buckling of columns under elastic compression wave. (Q1598204)

The authors derive two critical conditions for the dynamic buckling of columns on the base of the law of energy transformation and conservation at the instant when the dynamics occurs. The first condition is that the amount of the released compressive deformation energy must be equal to the sum of the buckling deformation energy and the buckling kinetic energy. The second condition is that the rate of energy transformation meets the energy conservation law in the instant course of the buckling. The governing equations, boundary and continuity conditions are derived bu using the first critical condition. A supplementary restraint equation at the front of the compression wave is derived by use of the second critical condition. The coupled characteristic equations for the two characteristic parameters are derived in accordance with the condition under which the governing equations together with boundary, continuity and supplementary restraint conditions have a nontrivial solution. The dynamic buckling modes, the critical load parameter and the dynamic characteristic parameter are calculated accurately from the solutions of the characteristic equations.