Instability of localised buckling modes in a one-dimensional strut model

Stability of localised equilibria arising in a fourth-order partial differential equation modelling struts is investigated. It was shown in Buffoni, Champneys & Toland (1996) that the model exhibits many multi-modal buckling states bifurcating from a primary buckling mode. In this article, using analytical and numerical techniques, the primary mode is shown to be unstable under dead loading in a large range of parameter values, while is likely to be stable under rigid loading for small axial loads. Furthermore, for general reversible or Hamiltonian systems, stability of the multi-modal solutions is established assuming stability of the primary state. As this hypothesis is not satisfied for the buckling mode arising in the strut model, any multi-modal buckling state will be unstable for both loading devices