CHAOTIC BEHAVIOR IN THE NON-LINEAR ELASTIC BEAM

摘要

The dynamic response of the non-linear elastic simply supported beam subjected to axial forces and transverse periodic load is studied. Melnikov method is used to consider the dynamic behavior of the system whose post-buckling path is steady and analyze specially the effect of the higher items in the controlling equation.The five-order items have great influence upon the dynamic behavior of the system. The result reveals that there exist either homoclinic orbits or heroclinic orbits in the system. In this paper, the critical value that the system enters chaotic states are given. The diagram of some example will be shown.