Twin-characteristic-parameter solution for dynamic buckling of columns under elastic compression wave

Abstract

Abstract Two critical conditions for the dynamic buckling of columns are derived on the basis of the consideration of energy transformation and conservation at the instant when the buckling occurs. The first critical condition is that the amount of released compressive deformation energy must be equal to the sum of buckling deformation energy and buckling kinetic energy in the instant course of the dynamic buckling. The second is that the rate of energy transformation meets the conservation law in the instant course. The governing equations, the boundary conditions and the continuity conditions derived by use of the first condition are the same as those obtained by use of Hamilton's theorem. These equations and conditions are insufficient for the determination of the critical load parameter and the exponent of transverse inertia term involved in the problem. A supplementary restraint equation at compression wave front is derived by use of the second condition. Two characteristic equations for the two parameters are derived by use of the solution of the governing equations and the above-mentioned restraint conditions. The two characteristic parameters and the corresponding buckling modes are calculated accurately from the solution of the characteristic equations. The simple formulas for the relation of the critical force with the buckling time are given. The theoretical results predicted by use of the formula are in reasonable agreement with the existent experiment results.