A Geometric Approach for Establishing Dynamic Buckling Loads of Autonomous Potential Two-Degree-of-Freedom Systems

Abstract

Nonlinear dynamic buckling of autonomous potential two-degree-of-freedom nondissipative systems with static unstable critical points lying on nonlinear primary equilibrium paths is studied via a geometric approach. This is based 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 criteria yield readily obtained “exact” dynamic buckling loads without solving the highly nonlinear initial-value problem. The simplicity, reliability, and efficiency of the proposed technique is illustrated with the aid of various dynamic buckling analyses of two two-degree-of-freedom models which are also compared with those obtained by the Verner-Runge-Kutta scheme.