INSTABILITY OF LOCALIZED BUCKLING MODES IN A ONE-DIMENSIONAL STRUT MODEL

Stability of localized solutions arising in a fourth-order differentia l equation modelling struts is investigated. It was shown by Buffoni e t al. in 1996 that the model exhibits many multimodal buckling states bifurcating from a primary buckling mode. In this article, using analy tical and numerical techniques, the primary mode is shown to be unstab le under dead loading for all axial loads, while it is likely to be st able under rigid loading for small axial loads. Furthermore, for gener al reversible or conservative systems, stability of the multimodal sol utions is established assuming stability of the primary state. Since t his hypothesis is not satisfied for the buckling mode arising in the s trut model, any multimodal buckling state will be unstable under dead and rigid loading.