DYNAMIC BUCKLING OF AN IMPERFECT COLUMN ON NONLINEAR FOUNDATION

A formal two-time perturbation expansion is used to study the dynamic response and buckling of a model imperfection-sensitive structure. A finite imperfect column resting on nonlinear elastic foundation subject to step loading is considered. A simple expression is obtained for the dynamic buckling load for small imperfections and small initial conditions. It is found that the effect of one Fourier coefficient in the expansion of the imperfection dominates in the asymptotic expression for the deflection and the dynamic buckling load. In certain previous papers, the imperfections are assumed to be in the shape of the classical buckling mode. In this analysis this restriction on the imperfection need not be made. The formal two-time procedure shows that imperfections in the shape of the classical buckling mode produce the greatest degradation in the dynamic buckling strength of the structure.