Chaotic behavior in the nonlinear elastic beam

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. The effect of the higher order terms in the controlling equation is taken into account. It is found that the fifth-order terms have a great influence on the dynamic behavior of the system The result shows that there exist either homoclinic orbits or heteroclinic orbits in the system In this paper, the critical values of the system entering chaotic states are given. The diagram of an example is shown.