A geometric approach for establishing dynamic buckling loads of autonomouspotential two-degree-of-freedom systems

Nonlinear dynamic buckling of autonomous potential two-degree-of-freedom no ndissipative systems with static unstable critical points lying on nonlinea r primary equilibrium paths is studied via a geometric approach. This is ba sed on certain salient properties of the zero level total potential energy "surface" which in conjunction with the total energy-balance equation allow establishment of new dynamic buckling criteria for planar systems. These c riteria yield readily obtained "exact" dynamic buckling loads without solvi ng the highly nonlinear initial-value problem. The simplicity,, reliability , and efficiency of the proposed technique is illustrated with the aid of v arious dynamic buckling analyses of two two-degree-of-freedom models which are also compared with those obtained by the Verner-Runge-Kutta scheme.