On the Buckling Modes and Buckling Load of an Infinitely Long but Harmonically Imperfect Column Lying on Cubic – Quintic Foundation

Abstract

This paper utilizes perturbation and asymptotic techniques to discuss and obtain, analytically, the buckling modes and buckling load of a harmonically imperfect column lying on an elastic foundation that has cubic – quintic nonlinearity. Two slightly different approaches are here utilized. In the first approach, the perturbation parameter is a component of the displacement while in the second approach, the perturbation is a component of the load. In the final assessment, results from both approaches are seen to be in good agreement. The results are however observed to be implicit in the load parameter and are valid asymptotically as long as these perturbation parameters are small relative to unity.