Static and Dynamic Stability of an Imperfect Beam

This paper concerns the stability of an imperfect beam resting on a nonlinear elastic foundation, subjected to axial loads. Two types of load are considered: a static load, and a dynamic load in the form of a step function of time. The effect on the critical load of initial geometric imperfections is obtained and comparisons are drawn between the static and dynamic results. Comparisons are also drawn between asymptotic results and extended results, where terms up to cubic in the initial imperfection and deflection are retained. It is shown that the form of the results for static and dynamic loads is very similar. Also, the ratio of the reduction in the dynamic and static critical loads, due to the presence of imperfections, appears to be more or less constant when the asymptotic and extended results are compared.