Cable Nonlinear Dynamics Analysis

This paper attempts to study the non-linear dynamics of cables. The nonlinear dynamics equations of cable are established by applying Newton method with geometric non-linearity taken into consideration. Applying simplified method and multi-scale method, the coupling vibration of the in-plane and outplane is studied. And the in-plane and out-plane vibration couples can be discovered when the cable抯 parameters satisfy certain conditions. In chapter 4. the single-degree-of-freedom response of a cable under the condition of movable boundary is studied. In this chapter, the simplified model under boundary condition is attained. Then the influences of boundary condition and quadratic non-linearity on non-linear dynamics of cables are analyzed. Meanwhile, we analyze the procession of the route from the periodic motion to chaos motion of cable via period-doubling bifurcation. In chapter 5, the chaotic motion of cable is studied by utilizing Melnikov method and simulates the chaotic motion digitally.