Bifurcation and chaos in a bilinear constrained column. Part Ⅱ: Chaotic dynamics

摘要

In this paper a chaotic analysis of the bilinear constrained column illustrated in part I is performed. The homoclinic solutions of the umperturbed situation are explicitly computed, and it is shown how the perturbation of these orbits may lead to chaotic dynamics. The chaotic analysis was performed by means of Melnikov's method. Three different types of chaos were found: "left-chaos", "full-chaos" and "right-chaos", and the respective chaotic resonances were computed. The influence of the axial load and of the forcing circular frequency Φ were analyzed. The inefficiency of the asymmetric structures with regard to protection from the chaotic motions is discussed. The design problem was investigated, and some practical rules were proposed.