By Ette, Anthony Monday
The dynamic buckling loads of some imperfection-sensitive elastic structures subjected to slowly varying time dependent loading are determined using perturbation procedures. First, we consider an elastically imperfect column resting on a softening nonlinear elastic foundation. The governing differential equation has two small parameters. We determine the dynamic buckling load of this column subjected to the stipulated loading for three different cases. The cases are when the small parameters are not related and when they are related first linearly and next quadratically in some way.